
gamma distribution 3
I am still working on the gamma distribution and first thank you so much for help without help i wouldn't be able to do the previous questions.
Unfortunately, I got stuck with another question TT
For Z distributed on R^3 with Z1, Z2, Z3 IID Z ~ exp(1)
if I have Z = Z2 / (Z1+Z3) then what is E(Z) and Var(Z)?
Since I was using the chisquare,
I got Z2 ~ exp(1) => Z2 ~ G(1) => 2Z2 ~ G(1,2) => X^2(2)/2
because Y ~ X^2(m) iff y = 2z, z ~ G(m/2) //G is gamma
In the similar manner I got Z1+Z3 ~ G(2) => X^2(4)/2
Thus, Z2 / (Z1+Z3) = [X^2(2)/2] / [X^2(4)/2] which becomes Fdist with (2,4)
Then HOW can I find the expected value of Z and Var(Z)????? Is there any equation to find Fdistribution's E value and Variance???
plz help me!!! TT