Question

Suppose X follows a Chi-square distribution with degree of freedom m = 5 so that E(X) = 5 and Var(X) = 10. Also, let Y = 4X - 10.

Find E(Y) and Var (Y).

Does Y follow a Chi-square distribution with degree of freedom m = 10?

Answer 1

We know, for any random variable Z if then, E(Z)=n and Var(Z)=2n.

  

Now we calculate mean and variance for Y=4X-10.

Now if then E(Y)=10 and Var(Y)=2*10=20. But this is not occurring here,

So, we can conclude that Y does not follow Chi-square distribution with degree of freedom m=10.