Question

The coefficient of correlation between two variables X and Y is -0.4 and their covariance is equal to -16 .If the variance of Y series is 36,find the variance of X series​

Answer 1

Answer:

given that,

r

xy

=0.48Var(x)=16cov(x,y)=36

r

xy

=

Var(x)⋅Var(y)

cov(x,y)

⇒0.48=

16×Var(y)

36

⇒2.304=

16×Var(y)

36×36

⇒Var(y)=

2.304×16

36×36

∴Var(y)=35.15

∴σ

y

=

Var(y)

=

35.15

=5.92