Question

Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20 if the variance of X is 25, the standard deviation of Y is ____

Answer 1

Answer:

0.16

Explanation:

Answer 2

Given : Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20

the variance of X is 25,

To Find :      the standard deviation of Y

Solution :

Correlation coefficient = cov (x,y)/ (std deviation (x) ×std deviation (y))

Correlation coefficient  = 0.8

cov (x,y) = 20

variance of X is 25.  

variance = (standard deviation ) ²

=> std deviation (X) = √variance  of X = √25 =5

Substituting values

=>  0.8  = 20 / ( 5 * std deviation (y))

=>  0.8  = 4 / std deviation (y))

=> std deviation (y) = 4 / ( 0.8)

=> std deviation (y) = 5

standard deviation of Y  is  =  5

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