# Two-dimensional Frequency Distribution: Multiple Choice Questions/en

1 Random variables are independent if:

 Cov(X,Y)=0. f(x,y)=f(x)f(y) for all x,y. there exists at least one x and one y such that ${\displaystyle f(x,y)=f(x)f(y)}$. f(x|y)=f(x) for all x,y. Corr(X,Y)=0.

2 The linear dependency between metrically scale random variables is the stronger,

 the greater is the correlation. the greater is the absolute value of the correlation. the greater is the covariance.

3 Assume that for the metrically scaled random variables ${\displaystyle X}$ and ${\displaystyle Y}$ we have: ${\displaystyle Y=aX+b}$, then:

 Corr(X,Y)=0. Cov(X,Y)=0. Corr(X,Y)=1. Corr(X,Y)=-1.

4 The joint distribution of variables X and Y is uniquely determined by their marginal distributions.

 False. True.

5 Contingency table for two nominal or ordinal variables X and Y contains

 conditional distribution of ${\displaystyle X}$ for given ${\displaystyle Y=y}$. marginal distribution of X and Y. joint discrete distribution of X and Y.

6 ${\displaystyle X}$ and ${\displaystyle Y}$ are two metrically scale random variables, ${\displaystyle a}$ and ${\displaystyle b}$ are real numbers. Then, the covariance ${\displaystyle Cov(a+X,bY)}$ is equal to

 ${\displaystyle bCov(X+a,Y)}$ ${\displaystyle Cov(X,bY)}$ ${\displaystyle a+Cov(X,bY)}$ ${\displaystyle Cov(bX,Y+a)}$ ${\displaystyle b^{2}Cov(a+X,Y)}$ ${\displaystyle bCov(X,Y)}$

7 The dependency between two ordinal variables can be assessed via the following tools:

 Bravais-Pearson correlation coefficient. correlation table. contingency table. scatterplot. rank correlation.

8 Scatterplot is used to visualize

 observed values of two metrically scaled variables. observed values of two ordinal variables. marginal distribution of two metric variables. joint discrete distribution of two cardinal variables.

1 Random variables are independent if:

 Cov(X,Y)=0. f(x,y)=f(x)f(y) for all x,y. there exists at least one x and one y such that ${\displaystyle f(x,y)=f(x)f(y)}$. f(x|y)=f(x) for all x,y. Corr(X,Y)=0.

2 The linear dependency between metrically scale random variables is the stronger,

 the greater is the correlation. the greater is the absolute value of the correlation. the greater is the covariance.

3 Assume that for the metrically scaled random variables ${\displaystyle X}$ and ${\displaystyle Y}$ we have: ${\displaystyle Y=aX+b}$, then:

 Corr(X,Y)=0. Cov(X,Y)=0. Corr(X,Y)=1. Corr(X,Y)=-1.

4 The joint distribution of variables X and Y is uniquely determined by their marginal distributions.

 False. True.

5 Contingency table for two nominal or ordinal variables X and Y contains

 conditional distribution of ${\displaystyle X}$ for given ${\displaystyle Y=y}$. marginal distribution of X and Y. joint discrete distribution of X and Y.

6 ${\displaystyle X}$ and ${\displaystyle Y}$ are two metrically scale random variables, ${\displaystyle a}$ and ${\displaystyle b}$ are real numbers. Then, the covariance ${\displaystyle Cov(a+X,bY)}$ is equal to

 ${\displaystyle bCov(X+a,Y)}$ ${\displaystyle Cov(X,bY)}$ ${\displaystyle a+Cov(X,bY)}$ ${\displaystyle Cov(bX,Y+a)}$ ${\displaystyle b^{2}Cov(a+X,Y)}$ ${\displaystyle bCov(X,Y)}$

7 The dependency between two ordinal variables can be assessed via the following tools:

 Bravais-Pearson correlation coefficient. correlation table. contingency table. scatterplot. rank correlation.

8 Scatterplot is used to visualize

 observed values of two metrically scaled variables. observed values of two ordinal variables. marginal distribution of two metric variables. joint discrete distribution of two cardinal variables.

1 Random variables are independent if:

 Cov(X,Y)=0. f(x,y)=f(x)f(y) for all x,y. there exists at least one x and one y such that ${\displaystyle f(x,y)=f(x)f(y)}$. f(x|y)=f(x) for all x,y. Corr(X,Y)=0.

2 The linear dependency between metrically scale random variables is the stronger,

 the greater is the correlation. the greater is the absolute value of the correlation. the greater is the covariance.

3 Assume that for the metrically scaled random variables ${\displaystyle X}$ and ${\displaystyle Y}$ we have: ${\displaystyle Y=aX+b}$, then:

 Corr(X,Y)=0. Cov(X,Y)=0. Corr(X,Y)=1. Corr(X,Y)=-1.

4 The joint distribution of variables X and Y is uniquely determined by their marginal distributions.

 False. True.

5 Contingency table for two nominal or ordinal variables X and Y contains

 conditional distribution of ${\displaystyle X}$ for given ${\displaystyle Y=y}$. marginal distribution of X and Y. joint discrete distribution of X and Y.

6 ${\displaystyle X}$ and ${\displaystyle Y}$ are two metrically scale random variables, ${\displaystyle a}$ and ${\displaystyle b}$ are real numbers. Then, the covariance ${\displaystyle Cov(a+X,bY)}$ is equal to

 ${\displaystyle bCov(X+a,Y)}$ ${\displaystyle Cov(X,bY)}$ ${\displaystyle a+Cov(X,bY)}$ ${\displaystyle Cov(bX,Y+a)}$ ${\displaystyle b^{2}Cov(a+X,Y)}$ ${\displaystyle bCov(X,Y)}$

7 The dependency between two ordinal variables can be assessed via the following tools:

 Bravais-Pearson correlation coefficient. correlation table. contingency table. scatterplot. rank correlation.

8 Scatterplot is used to visualize

 observed values of two metrically scaled variables. observed values of two ordinal variables. marginal distribution of two metric variables. joint discrete distribution of two cardinal variables.

1 Random variables are independent if:

 Cov(X,Y)=0. f(x,y)=f(x)f(y) for all x,y. there exists at least one x and one y such that ${\displaystyle f(x,y)=f(x)f(y)}$. f(x|y)=f(x) for all x,y. Corr(X,Y)=0.

2 The linear dependency between metrically scale random variables is the stronger,

 the greater is the correlation. the greater is the absolute value of the correlation. the greater is the covariance.

3 Assume that for the metrically scaled random variables ${\displaystyle X}$ and ${\displaystyle Y}$ we have: ${\displaystyle Y=aX+b}$, then:

 Corr(X,Y)=0. Cov(X,Y)=0. Corr(X,Y)=1. Corr(X,Y)=-1.

4 The joint distribution of variables X and Y is uniquely determined by their marginal distributions.

 False. True.

5 Contingency table for two nominal or ordinal variables X and Y contains

 conditional distribution of ${\displaystyle X}$ for given ${\displaystyle Y=y}$. marginal distribution of X and Y. joint discrete distribution of X and Y.

6 ${\displaystyle X}$ and ${\displaystyle Y}$ are two metrically scale random variables, ${\displaystyle a}$ and ${\displaystyle b}$ are real numbers. Then, the covariance ${\displaystyle Cov(a+X,bY)}$ is equal to

 ${\displaystyle bCov(X+a,Y)}$ ${\displaystyle Cov(X,bY)}$ ${\displaystyle a+Cov(X,bY)}$ ${\displaystyle Cov(bX,Y+a)}$ ${\displaystyle b^{2}Cov(a+X,Y)}$ ${\displaystyle bCov(X,Y)}$

7 The dependency between two ordinal variables can be assessed via the following tools:

 Bravais-Pearson correlation coefficient. correlation table. contingency table. scatterplot. rank correlation.

8 Scatterplot is used to visualize

 observed values of two metrically scaled variables. observed values of two ordinal variables. marginal distribution of two metric variables. joint discrete distribution of two cardinal variables.

1 Random variables are independent if:

 Cov(X,Y)=0. f(x,y)=f(x)f(y) for all x,y. there exists at least one x and one y such that ${\displaystyle f(x,y)=f(x)f(y)}$. f(x|y)=f(x) for all x,y. Corr(X,Y)=0.

2 The linear dependency between metrically scale random variables is the stronger,

 the greater is the correlation. the greater is the absolute value of the correlation. the greater is the covariance.

3 Assume that for the metrically scaled random variables ${\displaystyle X}$ and ${\displaystyle Y}$ we have: ${\displaystyle Y=aX+b}$, then:

 Corr(X,Y)=0. Cov(X,Y)=0. Corr(X,Y)=1. Corr(X,Y)=-1.

4 The joint distribution of variables X and Y is uniquely determined by their marginal distributions.

 False. True.

5 Contingency table for two nominal or ordinal variables X and Y contains

 conditional distribution of ${\displaystyle X}$ for given ${\displaystyle Y=y}$. marginal distribution of X and Y. joint discrete distribution of X and Y.

6 ${\displaystyle X}$ and ${\displaystyle Y}$ are two metrically scale random variables, ${\displaystyle a}$ and ${\displaystyle b}$ are real numbers. Then, the covariance ${\displaystyle Cov(a+X,bY)}$ is equal to

 ${\displaystyle bCov(X+a,Y)}$ ${\displaystyle Cov(X,bY)}$ ${\displaystyle a+Cov(X,bY)}$ ${\displaystyle Cov(bX,Y+a)}$ ${\displaystyle b^{2}Cov(a+X,Y)}$ ${\displaystyle bCov(X,Y)}$

7 The dependency between two ordinal variables can be assessed via the following tools:

 Bravais-Pearson correlation coefficient. correlation table. contingency table. scatterplot. rank correlation.

8 Scatterplot is used to visualize

 observed values of two metrically scaled variables. observed values of two ordinal variables. marginal distribution of two metric variables. joint discrete distribution of two cardinal variables.

1 Random variables are independent if:

 Cov(X,Y)=0. f(x,y)=f(x)f(y) for all x,y. there exists at least one x and one y such that ${\displaystyle f(x,y)=f(x)f(y)}$. f(x|y)=f(x) for all x,y. Corr(X,Y)=0.

2 The linear dependency between metrically scale random variables is the stronger,

 the greater is the correlation. the greater is the absolute value of the correlation. the greater is the covariance.

3 Assume that for the metrically scaled random variables ${\displaystyle X}$ and ${\displaystyle Y}$ we have: ${\displaystyle Y=aX+b}$, then:

 Corr(X,Y)=0. Cov(X,Y)=0. Corr(X,Y)=1. Corr(X,Y)=-1.

4 The joint distribution of variables X and Y is uniquely determined by their marginal distributions.

 False. True.

5 Contingency table for two nominal or ordinal variables X and Y contains

 conditional distribution of ${\displaystyle X}$ for given ${\displaystyle Y=y}$. marginal distribution of X and Y. joint discrete distribution of X and Y.

6 ${\displaystyle X}$ and ${\displaystyle Y}$ are two metrically scale random variables, ${\displaystyle a}$ and ${\displaystyle b}$ are real numbers. Then, the covariance ${\displaystyle Cov(a+X,bY)}$ is equal to

 ${\displaystyle bCov(X+a,Y)}$ ${\displaystyle Cov(X,bY)}$ ${\displaystyle a+Cov(X,bY)}$ ${\displaystyle Cov(bX,Y+a)}$ ${\displaystyle b^{2}Cov(a+X,Y)}$ ${\displaystyle bCov(X,Y)}$

7 The dependency between two ordinal variables can be assessed via the following tools:

 Bravais-Pearson correlation coefficient. correlation table. contingency table. scatterplot. rank correlation.

8 Scatterplot is used to visualize

 observed values of two metrically scaled variables. observed values of two ordinal variables. marginal distribution of two metric variables. joint discrete distribution of two cardinal variables.