# 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. - Mathematics and Statistics

Sum

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.

#### Solution

Given: r = 0.3, Cov (x, y) = 12,
sigma_"x"^2 = 9
∴ σx = 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.

Concept: Concept of Correlation Coefficient
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