Question

The cofficient of correlation between two varibles X and Y is 0.48.the convariance is 36.the variance of x is 16. Find the standard deviation of Y

Answer 1

Answer:

The standard deviation of Y is 18.75.

Step-by-step explanation:

The formula to compute the correlation coefficient is:

$Corr(X, Y)=\frac{Cov(X, Y)}{\sqrt{V(X)V(Y)}}$

Given:

Corr (X, Y) = 0.48

Cov (X, Y) = 36

V (X) = 16

Compute the standard deviation of Y as follows:

$Corr(X, Y)=\frac{Cov(X, Y)}{\sqrt{V(X)V(Y)}}\\0.48=\frac{36}{\sqrt{16\times V(Y)}}\\\sqrt{16\times V(Y)}=\frac{36}{0.48}\\4\times SD(Y)=75\\SD(Y)=18.75$

Thus, the standard deviation of Y is 18.75.