Question

The correlation coefficient between two variables x and y are 0.48. The covariance is 36 and the variance of x is 16. Find the standard deviation of y.

Answer 1

Given, r = 0.48, Cov (x, y) = 36
Since `sigma_"x"^2` = 16
∴ `sigma_"x"` = 4

Since, r = `("Cov"("x","y"))/(sigma_"x"sigma_"y")`

∴ 0.48 = `36/(4 xx sigma_"y")`

∴ `sigma_"y" = 36/(4 xx 0.48)=9/0.48`

= `900/48` = 18.75

∴Standard deviation of y is 18.75.