Question

The Karl Pearson's coefficient of correlation in between two variables X and Y is 1, covariance of X and Y is 6 and variance of X is 9 then what is the value of standard deviation of Y?​

Answer 1

Answer:

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Answer 2

Answer:

standard deviation of Y = 2

Step-by-step explanation:

Karl pearson's correlation coefficient is given by,

r = cov(X,Y)/(sigma X × sigma Y)

here Cov (X,Y) = 6,

variance of X = 9,

⇒ sigma X = √9

= 3

and r = 1

substituting the values, we will get

1 = 6/(3* sigma Y)

⇒ (3*sigma Y) = 6

⇒ sigma Y = 6/3

= 2

therefore sigma Y is 2

sigma Y is the standard deviation

∴ standard deviation of Y = 2

variance of Y = 2^2 (∵ variance = (SD)^2 )

variance of Y = 4