Question

if the covariancebetween two variables is 20 and variance of one of the variable is 16 what would be the variance of other variable ​

Answer 1

Answer:

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.

Answer 2

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.