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Normalverteilung - Versionsgeschichte
2024-03-28T12:43:11Z
Versionsgeschichte dieser Seite in MM*Stat
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https://wikis.hu-berlin.de/mmstat/w/index.php?title=Normalverteilung&diff=1227&oldid=prev
Jacobdan am 28. Mai 2018 um 13:17 Uhr
2018-05-28T13:17:48Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 28. Mai 2018, 14:17 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l73">Zeile 73:</td>
<td colspan="2" class="diff-lineno">Zeile 73:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die nachfolgenden Abbildungen zeigen gesondert die [[Dichtefunktion (eindimensional)|Dichtefunktion]] und die [[Verteilungsfunktion (stochastisch, eindimensional)|Verteilungsfunktion]] der <math>N(2;1)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die nachfolgenden Abbildungen zeigen gesondert die [[Dichtefunktion (eindimensional)|Dichtefunktion]] und die [[Verteilungsfunktion (stochastisch, eindimensional)|Verteilungsfunktion]] der <math>N(2;1)</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><iframe k="wiwi" p="examples/stat_Normalverteilung_Dichtefunktion_N2_1_R00480004800000000000000_plot.html"/></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><iframe k="wiwi" p="examples/stat_Normalverteilung_Dichtefunktion_N2_1_R00480004800000000000000_plot.html<ins style="font-weight: bold; text-decoration: none;">" align="left</ins>"/></div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><iframe k="wiwi" p="examples/stat_Normalverteilung_Verteilungsfunktion_N2_1_R00480004800000000000000_plot.html"/></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Weitere Eigenschaften der Normalverteilung===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Weitere Eigenschaften der Normalverteilung===</div></td></tr>
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Jacobdan
https://wikis.hu-berlin.de/mmstat/w/index.php?title=Normalverteilung&diff=1226&oldid=prev
Jacobdan am 28. Mai 2018 um 12:58 Uhr
2018-05-28T12:58:34Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 28. Mai 2018, 13:58 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61">Zeile 61:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die folgende Grafik zeigt 5 [[Dichtefunktion (eindimensional)|Dichtefunktionen]] der Normalverteilung mit verschiedenen [[Parameter]]werten für <math>\mu</math> und <math>\sigma</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die folgende Grafik zeigt 5 [[Dichtefunktion (eindimensional)|Dichtefunktionen]] der Normalverteilung mit verschiedenen [[Parameter]]werten für <math>\mu</math> und <math>\sigma</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><iframe k="wiwi" p="examples<del style="font-weight: bold; text-decoration: none;">?P=stat</del>/<del style="font-weight: bold; text-decoration: none;">Normalverteilung/Normalverteilung_Dichte</del>.<del style="font-weight: bold; text-decoration: none;">R&V=P</del>" /></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><iframe k="wiwi" p="examples/<ins style="font-weight: bold; text-decoration: none;">stat_Normalverteilung_Eigenschaften_Dichte_R00480004800000000000000_plot</ins>.<ins style="font-weight: bold; text-decoration: none;">html</ins>" /></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der [[Parameter]] <math>\mu</math> beeinflusst die Lage der [[Verteilung (stochastisch)|Verteilung]] über der Abszisse. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der [[Parameter]] <math>\mu</math> beeinflusst die Lage der [[Verteilung (stochastisch)|Verteilung]] über der Abszisse. </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l73">Zeile 73:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die nachfolgenden Abbildungen zeigen gesondert die [[Dichtefunktion (eindimensional)|Dichtefunktion]] und die [[Verteilungsfunktion (stochastisch, eindimensional)|Verteilungsfunktion]] der <math>N(2;1)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die nachfolgenden Abbildungen zeigen gesondert die [[Dichtefunktion (eindimensional)|Dichtefunktion]] und die [[Verteilungsfunktion (stochastisch, eindimensional)|Verteilungsfunktion]] der <math>N(2;1)</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{| </del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><<ins style="font-weight: bold; text-decoration: none;">iframe k</ins>="<ins style="font-weight: bold; text-decoration: none;">wiwi</ins>" <ins style="font-weight: bold; text-decoration: none;">p="examples/stat_Normalverteilung_Dichtefunktion_N2_1_R00480004800000000000000_plot.html"/</ins>></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|</del><<del style="font-weight: bold; text-decoration: none;">R output</del>="<del style="font-weight: bold; text-decoration: none;">display</del>"></div></td><td colspan="2" class="diff-side-added"></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-2, to=6, dnorm(x, mean=2, sd=1), ylab="f(x)", col="darkgreen", main</del>="<del style="font-weight: bold; text-decoration: none;">Dichtefunktion der N(2; 1)</del>"<del style="font-weight: bold; text-decoration: none;">, ylim</del>=<del style="font-weight: bold; text-decoration: none;">c(0.00,0.4), lty=1, lwd=4, font.lab=2, </del>"<del style="font-weight: bold; text-decoration: none;">xaxs"="i" ,"yaxs"="i", bty="l")</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><iframe k</ins>="<ins style="font-weight: bold; text-decoration: none;">wiwi</ins>" <ins style="font-weight: bold; text-decoration: none;">p</ins>="<ins style="font-weight: bold; text-decoration: none;">examples</ins>/<ins style="font-weight: bold; text-decoration: none;">stat_Normalverteilung_Verteilungsfunktion_N2_1_R00480004800000000000000_plot</ins>.<ins style="font-weight: bold; text-decoration: none;">html</ins>"/></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><</del>/<del style="font-weight: bold; text-decoration: none;">R></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|<R output="display"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">pdf(rpdf,width=7,height=7)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-2, to=6, pnorm(x, mean=2, sd=1), ylab="F(x)", col="darkgreen", main="Verteilungsfunktion der N(2; 1)", ylim=c(0</del>.<del style="font-weight: bold; text-decoration: none;">00,1.0), lty=1, lwd=4, font.lab=2, </del>"<del style="font-weight: bold; text-decoration: none;">xaxs"="i" ,"yaxs"="i", bty="l")</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><</del>/<del style="font-weight: bold; text-decoration: none;">R</del>></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|}</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Weitere Eigenschaften der Normalverteilung===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Weitere Eigenschaften der Normalverteilung===</div></td></tr>
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<td colspan="2" class="diff-lineno">Zeile 86:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die folgende Grafik zeigt diese Eigenschaften für die <math>N(2;1)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die folgende Grafik zeigt diese Eigenschaften für die <math>N(2;1)</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{|</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><<ins style="font-weight: bold; text-decoration: none;">iframe k</ins>="<ins style="font-weight: bold; text-decoration: none;">wiwi</ins>" <ins style="font-weight: bold; text-decoration: none;">p</ins>="<ins style="font-weight: bold; text-decoration: none;">examples/stat_Normalverteilung_Eigenschaften_Dichte_R00480004800000000000000_plot</ins>.<ins style="font-weight: bold; text-decoration: none;">html</ins>"/></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|</del><<del style="font-weight: bold; text-decoration: none;">R output="display"></del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><<ins style="font-weight: bold; text-decoration: none;">iframe k</ins>="<ins style="font-weight: bold; text-decoration: none;">wiwi</ins>" <ins style="font-weight: bold; text-decoration: none;">p</ins>="<ins style="font-weight: bold; text-decoration: none;">examples/stat_Normalverteilung_Eigenschaften_Verteilung_R00480004800000000000000_plot</ins>.<ins style="font-weight: bold; text-decoration: none;">html</ins>"/></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">pdf(rpdf,width=7,height=7)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-2, to=6, dnorm(x, mean=2, sd=1), xaxt</del>="<del style="font-weight: bold; text-decoration: none;">n</del>"<del style="font-weight: bold; text-decoration: none;">, ylab</del>="<del style="font-weight: bold; text-decoration: none;">f(x)", xlab="x", col="black", ylim=c(0</del>.<del style="font-weight: bold; text-decoration: none;">0,0.4), lty=1, lwd=4, font.lab=2, "xaxs"="i" ,"yaxs"="i", bty="l</del>"<del style="font-weight: bold; text-decoration: none;">)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">abline(v=1, lwd=2)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">abline(v=2, lwd=2)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">abline(v=3, lwd=2)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">axis(at=c(-2:6), side=1, tick=TRUE, labels=FALSE, lwd.ticks=2)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><</del>/<del style="font-weight: bold; text-decoration: none;">R</del>></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|</del><<del style="font-weight: bold; text-decoration: none;">R output="display"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">pdf(rpdf,width=7,height=7)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-2, to=6, pnorm(x, mean=2, sd=1), xaxt</del>="<del style="font-weight: bold; text-decoration: none;">n</del>"<del style="font-weight: bold; text-decoration: none;">, ylab</del>="<del style="font-weight: bold; text-decoration: none;">F(x)", xlab="x", col="black", ylim=c(0.0,1.0), lty=1, lwd=4, font</del>.<del style="font-weight: bold; text-decoration: none;">lab=2, "xaxs"="i" ,"yaxs"="i", bty="l</del>"<del style="font-weight: bold; text-decoration: none;">)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">abline(v=1, lwd=2)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">abline(v=2, lwd=2)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">abline(v=3, lwd=2)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">abline(h=0.5, lwd=2, lty=3)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">axis(at=c(-2:6), side=1, tick=TRUE, labels=TRUE, lwd.ticks=2)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><</del>/<del style="font-weight: bold; text-decoration: none;">R</del>></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|}</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
</table>
Jacobdan
https://wikis.hu-berlin.de/mmstat/w/index.php?title=Normalverteilung&diff=396&oldid=prev
Jacobdan am 23. Mai 2018 um 10:34 Uhr
2018-05-23T10:34:18Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="de-x-formal">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 23. Mai 2018, 11:34 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61">Zeile 61:</td>
<td colspan="2" class="diff-lineno">Zeile 61:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die folgende Grafik zeigt 5 [[Dichtefunktion (eindimensional)|Dichtefunktionen]] der Normalverteilung mit verschiedenen [[Parameter]]werten für <math>\mu</math> und <math>\sigma</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die folgende Grafik zeigt 5 [[Dichtefunktion (eindimensional)|Dichtefunktionen]] der Normalverteilung mit verschiedenen [[Parameter]]werten für <math>\mu</math> und <math>\sigma</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><iframe k="wiwi" p="examples?P=stat/Normalverteilung/Normalverteilung_Dichte.R" /></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><iframe k="wiwi" p="examples?P=stat/Normalverteilung/Normalverteilung_Dichte.R<ins style="font-weight: bold; text-decoration: none;">&V=P</ins>" /></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der [[Parameter]] <math>\mu</math> beeinflusst die Lage der [[Verteilung (stochastisch)|Verteilung]] über der Abszisse. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der [[Parameter]] <math>\mu</math> beeinflusst die Lage der [[Verteilung (stochastisch)|Verteilung]] über der Abszisse. </div></td></tr>
</table>
Jacobdan
https://wikis.hu-berlin.de/mmstat/w/index.php?title=Normalverteilung&diff=395&oldid=prev
Jacobdan am 20. Mai 2018 um 09:21 Uhr
2018-05-20T09:21:24Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="de-x-formal">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 20. Mai 2018, 10:21 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61">Zeile 61:</td>
<td colspan="2" class="diff-lineno">Zeile 61:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die folgende Grafik zeigt 5 [[Dichtefunktion (eindimensional)|Dichtefunktionen]] der Normalverteilung mit verschiedenen [[Parameter]]werten für <math>\mu</math> und <math>\sigma</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die folgende Grafik zeigt 5 [[Dichtefunktion (eindimensional)|Dichtefunktionen]] der Normalverteilung mit verschiedenen [[Parameter]]werten für <math>\mu</math> und <math>\sigma</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{| </del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><<ins style="font-weight: bold; text-decoration: none;">iframe k</ins>="<ins style="font-weight: bold; text-decoration: none;">wiwi</ins>" <ins style="font-weight: bold; text-decoration: none;">p</ins>="<ins style="font-weight: bold; text-decoration: none;">examples?P</ins>=<ins style="font-weight: bold; text-decoration: none;">stat/Normalverteilung</ins>/<ins style="font-weight: bold; text-decoration: none;">Normalverteilung_Dichte</ins>.<ins style="font-weight: bold; text-decoration: none;">R</ins>" /></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|</del><<del style="font-weight: bold; text-decoration: none;">R output</del>="<del style="font-weight: bold; text-decoration: none;">display</del>"<del style="font-weight: bold; text-decoration: none;">></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">pdf(rpdf,width=7,height=7)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-6, to=6, dnorm(x, mean=0, sd</del>=<del style="font-weight: bold; text-decoration: none;">1), ylab="f(x)</del>"<del style="font-weight: bold; text-decoration: none;">, col</del>=<del style="font-weight: bold; text-decoration: none;">"black", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">par(new=TRUE)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-6, to=6, dnorm(x, mean=0, sd=(1</del>/<del style="font-weight: bold; text-decoration: none;">3)), ylab="f(x)", col="green", ylim=c(0</del>.<del style="font-weight: bold; text-decoration: none;">0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">par(new=TRUE)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-6, to=6, dnorm(x, mean=0, sd=2), ylab="f(x)", col="blue", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">par(new=TRUE)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-6, to=6, dnorm(x, mean=1, sd=1), ylab="f(x)", col="red", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"=</del>"<del style="font-weight: bold; text-decoration: none;">i" ,"yaxs"="i", bty="l")</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">par(new=TRUE)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">curve(from=-6, to=6, dnorm(x, mean=2, sd=1), ylab="f(x)", col="darkgreen", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">par(new=TRUE)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">legend("topright", lwd=4, col=c("black","green","blue","red","darkgreen"),c("N(0;1)","N(0;1</del>/<del style="font-weight: bold; text-decoration: none;">3)","N(0;2)","N(1;1)","N(2;1)"), bty="n")</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></R</del>></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|}</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der [[Parameter]] <math>\mu</math> beeinflusst die Lage der [[Verteilung (stochastisch)|Verteilung]] über der Abszisse. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der [[Parameter]] <math>\mu</math> beeinflusst die Lage der [[Verteilung (stochastisch)|Verteilung]] über der Abszisse. </div></td></tr>
</table>
Jacobdan
https://wikis.hu-berlin.de/mmstat/w/index.php?title=Normalverteilung&diff=352&oldid=prev
Jacobdan: Die Seite wurde neu angelegt: „{{Verteilungsmodelle}} =={{Vorlage:Überschrift}}== ===Normalverteilung oder Gauß-Verteilung=== Eine stetige Zufallsvariable <math>X</math> heißt ''no…“
2018-05-18T12:21:50Z
<p>Die Seite wurde neu angelegt: „{{Verteilungsmodelle}} =={{Vorlage:Überschrift}}== ===Normalverteilung oder Gauß-Verteilung=== Eine <a href="/mmstat/Stetige_Zufallsvariable" class="mw-redirect" title="Stetige Zufallsvariable">stetige Zufallsvariable</a> <math>X</math> heißt ''no…“</p>
<p><b>Neue Seite</b></p><div>{{Verteilungsmodelle}}<br />
<br />
=={{Vorlage:Überschrift}}==<br />
<br />
===Normalverteilung oder Gauß-Verteilung===<br />
<br />
Eine [[stetige Zufallsvariable]] <math>X</math> heißt ''normalverteilt'' mit den Parametern <math>\mu</math> und <math>\sigma</math>, abgekürzt <math>X\sim N(\mu,\sigma)\,</math>, wenn ihre [[Dichtefunktion (eindimensional)|Dichtefunktion]] gegeben ist durch:<br />
<br />
<math>f_{NV}(x;\mu ,\sigma )=\frac{1}{\sigma \sqrt{2\pi }}e^{-(x-\mu )^{2}/2\sigma ^{2}}\quad \mbox{, wenn } -\infty<x<+\infty ,\ \sigma >0</math><br />
<br />
die [[Verteilungsfunktion (stochastisch, eindimensional)|Verteilungsfunktion]] ist gegeben durch:<br />
<br />
<math>F_{NV}(x;\mu ,\sigma )=\frac{1}{\sigma \sqrt{2\pi }}\int\limits_{-\infty }^{x}e^{-(t-\mu)^{2}/2\sigma ^{2}}\;dt</math><br />
<br />
Aus der [[Dichtefunktion (eindimensional)|Dichtefunktion]] bzw. der [[Verteilungsfunktion (stochastisch, eindimensional)|Verteilungsfunktion]] ist erkennbar, dass die ''Normalverteilung'' von den beiden [[Parameter]]n <math>\mu</math> und <math>\sigma</math> abhängt.<br />
<br />
Diese [[Parameter]] sind der [[Erwartungswert]] und die [[Standardabweichung (stochastisch)|Standardabweichung]] der [[Zufallsvariable]]n <math>X</math>.<br />
<br />
Die Normalverteilung wird auch als ''Gauß-Verteilung'' bezeichnet.<br />
<br />
Sie ist die wichtigste [[Stetiges Merkmal|stetige]] [[Verteilung (stochastisch)|Verteilung]], weil<br />
<br />
* bei vielen praktischen Anwendungen zumindest näherungsweise die Verteilungsgestalt einer Normalverteilung vorliegt;<br />
* sie eine approximative Bestimmung vieler anderer [[Verteilung (stochastisch)|Verteilungen]] ermöglicht;<br />
* sie bei einer Vielzahl von statistischen Maßzahlen als Verteilungsmodell unterstellt werden kann, wenn der [[Datensatz]] groß genug ist.<br />
<br />
Eine normalverteilte [[Zufallsvariable]] kann theoretisch alle Werte zwischen <math>-\infty</math> und <math>+\infty</math> annehmen, d.h. ihr Wertebereich ist nach oben und unten unbegrenzt.<br />
<br />
===Gauß'sche Glockenkurve===<br />
<br />
Die [[Dichtefunktion (eindimensional)|Dichtefunktion]] einer [[Gauß-Verteilung]] wird auch als ''Gauß'sche Glockenkurve'' bezeichnet. Sie ist gegeben durch:<br />
<br />
<math>f_{NV}(x;\mu ,\sigma )=\frac{1}{\sigma \sqrt{2\pi }}e^{-(x-\mu )^{2}/2\sigma ^{2}}\quad \mbox{, wenn } -\infty<x<+\infty ,\ \sigma >0</math><br />
<br />
=={{Vorlage:Überschrift_2}}==<br />
<br />
===Lineare Transformation===<br />
<br />
Sei <math>X</math> normalverteilt, <math>X\sim N\,(\mu ,\sigma )</math> und <math>Y</math> die durch eine Linearkombination erhaltene [[Zufallsvariable]] <math>Y = a + b\cdot X</math> mit <math>b\neq 0</math>, dann ist <math>Y</math> wieder normalverteilt mit <math>Y \sim N(a + b \mu,\;|b| \cdot \sigma)</math><br />
<br />
Durch die Linearkombination ändert sich der Verteilungstyp nicht. <br />
<br />
Die Werte der [[Parameter]] der transformierten [[Variable]]n ergeben sich dabei aus den Rechenregeln für den [[Erwartungswert]] und die [[Varianz (stochastisch)|Varianz]]:<br />
<br />
<math>E[a + b\cdot X] = a + b \cdot E[X]</math><br />
<br />
<math>Var(a + b\cdot X) = b^2\cdot Var(X) = b^2\cdot {\sigma}^2</math>.<br />
<br />
===Reproduktivitätseigenschaft===<br />
<br />
Gegeben seien <math>n</math> [[Zufallsvariable]]n <math>X_1,X_2 \ldots,X_n</math> die identisch normalverteilt sind: <math>X_i \sim N(\mu_i,\sigma_i),\; E[X_i] = \mu_i,\; Var(X_i) = \sigma_i^2</math>.<br />
<br />
Die Summe [[Unabhängigkeit (stochastisch)|unabhängiger]], normalverteilter [[Zufallsvariable]]n <math>X_1, \ldots, X_n</math>, d.h.<br />
<br />
<math>Y = a_1X_1 + a_2X_2 + \ldots + a_nX_n</math> mit <math>a_i \neq 0</math> für mindestens ein <math>i</math>, ist wieder normalverteilt:<br />
<br />
<math>Y = \sum\limits_{i=1}^na_iX_i \sim N\left(\sum\limits_{i=1}^na_i\mu_i, \sqrt{\sum\limits_{i=1}^n a_i^2\sigma_i^2}\right)</math><br />
<br />
===Graphische Darstellung der Normalverteilung===<br />
<br />
Die folgende Grafik zeigt 5 [[Dichtefunktion (eindimensional)|Dichtefunktionen]] der Normalverteilung mit verschiedenen [[Parameter]]werten für <math>\mu</math> und <math>\sigma</math>.<br />
<br />
{| <br />
|<R output="display"><br />
pdf(rpdf,width=7,height=7)<br />
<br />
curve(from=-6, to=6, dnorm(x, mean=0, sd=1), ylab="f(x)", col="black", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")<br />
par(new=TRUE)<br />
curve(from=-6, to=6, dnorm(x, mean=0, sd=(1/3)), ylab="f(x)", col="green", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")<br />
par(new=TRUE)<br />
curve(from=-6, to=6, dnorm(x, mean=0, sd=2), ylab="f(x)", col="blue", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")<br />
par(new=TRUE)<br />
curve(from=-6, to=6, dnorm(x, mean=1, sd=1), ylab="f(x)", col="red", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")<br />
par(new=TRUE)<br />
curve(from=-6, to=6, dnorm(x, mean=2, sd=1), ylab="f(x)", col="darkgreen", ylim=c(0.0,1.2), lty=1, lwd=4, font.lab=2,"xaxs"="i" ,"yaxs"="i", bty="l")<br />
par(new=TRUE)<br />
<br />
legend("topright", lwd=4, col=c("black","green","blue","red","darkgreen"),c("N(0;1)","N(0;1/3)","N(0;2)","N(1;1)","N(2;1)"), bty="n")<br />
<br />
</R><br />
|}<br />
<br />
Der [[Parameter]] <math>\mu</math> beeinflusst die Lage der [[Verteilung (stochastisch)|Verteilung]] über der Abszisse. <br />
<br />
Durch Veränderung von <math>\mu</math> verschiebt sich die komplette Kurve ohne Veränderung ihrer Gestalt. <br />
<br />
Durch Vergrößerung bzw. Verkleinerung des [[Parameter]]s <math>\sigma</math> wird die [[Dichtefunktion (eindimensional)|Dichtefunktion]] auseinandergezogen bzw. zusammengedrückt, gleichzeitig sinkt bzw. steigt das Maximum. <br />
<br />
Je größer <math>\sigma</math> ist, desto flacher und breiter ist die Kurve, je kleiner <math>\sigma</math> desto schmaler und höher ist die Kurve.<br />
<br />
Die nachfolgenden Abbildungen zeigen gesondert die [[Dichtefunktion (eindimensional)|Dichtefunktion]] und die [[Verteilungsfunktion (stochastisch, eindimensional)|Verteilungsfunktion]] der <math>N(2;1)</math>.<br />
<br />
{| <br />
|<R output="display"><br />
pdf(rpdf,width=7,height=7)<br />
<br />
curve(from=-2, to=6, dnorm(x, mean=2, sd=1), ylab="f(x)", col="darkgreen", main="Dichtefunktion der N(2; 1)", ylim=c(0.00,0.4), lty=1, lwd=4, font.lab=2, "xaxs"="i" ,"yaxs"="i", bty="l")<br />
<br />
</R><br />
<br />
|<R output="display"><br />
pdf(rpdf,width=7,height=7)<br />
<br />
curve(from=-2, to=6, pnorm(x, mean=2, sd=1), ylab="F(x)", col="darkgreen", main="Verteilungsfunktion der N(2; 1)", ylim=c(0.00,1.0), lty=1, lwd=4, font.lab=2, "xaxs"="i" ,"yaxs"="i", bty="l")<br />
<br />
</R><br />
|}<br />
<br />
===Weitere Eigenschaften der Normalverteilung===<br />
<br />
* Die [[Dichtefunktion (eindimensional)|Dichtefunktion]] hat ihr globales Maximum ([[Modus]]) im Punkte <math>x = \mu</math><br />
* Die [[Dichtefunktion (eindimensional)|Dichtefunktion]] ist symmetrisch im Punkt <math>x = \mu</math>. Aus der Symmetrie folgt, dass auch der [[Median]] <math>x_{0.5}=\mu </math> ist.<br />
* Die [[Dichtefunktion (eindimensional)|Dichtefunktion]] hat an den Stellen <math>x_{1}=\mu -\sigma</math> und <math>x_{2}=\mu +\sigma </math> je einen Wendepunkt.<br />
* Für <math>x\rightarrow -\infty </math> und <math>x\rightarrow \infty </math> nähert sich die [[Dichtefunktion (eindimensional)|Dichtefunktion]] asymptotisch dem Wert 0.<br />
<br />
Die folgende Grafik zeigt diese Eigenschaften für die <math>N(2;1)</math>.<br />
<br />
{|<br />
|<R output="display"><br />
pdf(rpdf,width=7,height=7)<br />
<br />
curve(from=-2, to=6, dnorm(x, mean=2, sd=1), xaxt="n", ylab="f(x)", xlab="x", col="black", ylim=c(0.0,0.4), lty=1, lwd=4, font.lab=2, "xaxs"="i" ,"yaxs"="i", bty="l")<br />
abline(v=1, lwd=2)<br />
abline(v=2, lwd=2)<br />
abline(v=3, lwd=2)<br />
axis(at=c(-2:6), side=1, tick=TRUE, labels=FALSE, lwd.ticks=2)<br />
<br />
</R><br />
<br />
|<R output="display"><br />
pdf(rpdf,width=7,height=7)<br />
<br />
curve(from=-2, to=6, pnorm(x, mean=2, sd=1), xaxt="n", ylab="F(x)", xlab="x", col="black", ylim=c(0.0,1.0), lty=1, lwd=4, font.lab=2, "xaxs"="i" ,"yaxs"="i", bty="l")<br />
abline(v=1, lwd=2)<br />
abline(v=2, lwd=2)<br />
abline(v=3, lwd=2)<br />
abline(h=0.5, lwd=2, lty=3)<br />
axis(at=c(-2:6), side=1, tick=TRUE, labels=TRUE, lwd.ticks=2)<br />
<br />
</R><br />
|}</div>
Jacobdan