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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.
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Solution
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.
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