F - Distribution

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Consider two independent random variables , with degrees of freedom respectively, then the random variable: will have a F-distribution (denoted as )with parameters and . The and parameters represent the degrees of freedom for the distributed random variables in the numerator and the denominator. An F-distribution with parameters , has expected value and variance This diagram plots some F-distributions for different values of .

Nl s2 29c 3.gif

The Chi-square, t-, and F- distributions are distributions that are functions of Normal random variables that are particularly useful in statistics. On the F-Distribution. The density function of an F-distribution is right-skewed. Increasing the values of and reduces this skewness. As and , the density of the F-distribution will tend to a standard Normal distribution. The F-distribution is plotted for different values of and .