Please give true/false answers to these questions
1. The conditional variance of the random variable Y given that X = x, in the case of discrete
random variables, is found as V(Y|x) = Syy^2fY|x(y) (where Sy denotes the sum over y).
2. If X and Y are independent, then fY(y) does not equal fY|x(y).
3. The covariance of two random variables is a measure of the relationship between them
4. If X and Y are positively correlated, then there is not a linear relationship between them.
5. If Y and X are independent random variables, then the correlation between them is zero.
Solution
1. The conditional variance of the random variable Y given that X = x, in the case of discrete
random variables, is found as V(Y|x) = Syy^2fY|x(y) (where Sy denotes the sum over y).
Answer: True
2. If X and Y are independent, then fY(y) does not equal fY|x(y).
Answer: False
Since f(y/x)=f(x,y)/f(x)
=f(x)f(y)/f(x)
=f(y)
So it\'sequal to f(y)
3. The covariance of two random variables is a measure of the relationship between them
Answer: True
4. If X and Y are positively correlated, then there is not a linear relationship between them.
Answer: False
5. If Y and X are independent random variables, then the correlation between them is zero.
Answer: True
.
Presiding Officer Training module 2024 lok sabha elections
True/false questions on random variables
1. Please give true/false answers to these questions
1. The conditional variance of the random variable Y given that X = x, in the case of discrete
random variables, is found as V(Y|x) = Syy^2fY|x(y) (where Sy denotes the sum over y).
2. If X and Y are independent, then fY(y) does not equal fY|x(y).
3. The covariance of two random variables is a measure of the relationship between them
4. If X and Y are positively correlated, then there is not a linear relationship between them.
5. If Y and X are independent random variables, then the correlation between them is zero.
Solution
1. The conditional variance of the random variable Y given that X = x, in the case of discrete
random variables, is found as V(Y|x) = Syy^2fY|x(y) (where Sy denotes the sum over y).
Answer: True
2. If X and Y are independent, then fY(y) does not equal fY|x(y).
Answer: False
Since f(y/x)=f(x,y)/f(x)
=f(x)f(y)/f(x)
=f(y)
So it'sequal to f(y)
3. The covariance of two random variables is a measure of the relationship between them
Answer: True
4. If X and Y are positively correlated, then there is not a linear relationship between them.
Answer: False
5. If Y and X are independent random variables, then the correlation between them is zero.
Answer: True
