Question

If the standard deviation of x is 15, the covariance of x and y is 94.5, the coefficient of correlation r = 0.90, then the variance of y is 7.0.
a. True
b. False

Answer 1

We have the formula

$Cov(X,Y)=\rho_{X,Y}\sqrt{Var(X)Var(Y)}$

From the above formula,

$Var(Y)=\frac{Cov(X,Y)^2}{\rho_{X,Y} ^2Var(X)}\\ Var(Y)=\frac{94.5^2}{0.9 ^215^2}\\ Var(Y)=49$

That is variance of Y is 49 not 7.

Hence the statement is (b) False