If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?
  • a)
    More than 100
  • b)
    More than 10
  • c)
    Less than 10
  • d)
    More than 1.25
Correct answer is option 'A'. Can you explain this answer?

CA Foundation Question

Given, Cov (x, y) =20
and variance of one of the variables is 16.

so the standard deviation SD is 4.

we know the formula,
r= cov (x, y) /(SD of x * SD of Y)
r= 20 /4 * SD of the other variable
r= 5/ SD of the other variable

we also know that coefficient of correlation, r, lies between -1 and +1 including them.

so, SD of the other variable has to be atleast 5 or more.

so the variance will be 5^2 = 25 atleast or more.


i dont know why the icai book says the answer is more than 100. if anybody can match the answer with book then please tell me.

Aryan Dubey
Sep 12, 2019
I think answer is d

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