Question

Correlation coefficient between x and y is 0.3 and their covariance is 12. The variance of x is 9, Find the standard deviation of y.

Answer 1

Given: r = 0.3, Cov (x, y) = 12,
`sigma_"x"^2` = 9
∴ σ_x = 3
Karl Pearson’s coefficient of correlation,

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

∴ 0.3 = `12/(3 xx sigma_"y")`

∴ `sigma_"y" = 12/(3 xx 0.3)`
∴ `sigma_"y"=4/0.3`
∴ `sigma_"y"` = 13.33
∴ The standard deviation of y is 13.33.