Answer to Question #21179 in Statistics and Probability for Your name...

Question

let the r.v X have gamma distribution with parameters α and β
(i) show that EX= αβ , var(x) = α*β^2
(ii) As a special case of part (i) show that: If X has negative exponential distribution woth parameter λ then EX= 1/λ , Var(x) = 1/λ^2
(iii) If X~ X X^2r (r is not multiply by 2) then EX=r , Var(x) = 2*r