if x distributed as Poisson distribution with parameter lambda=5 find:
1- moment generating function of (3x-2)
2- the mean and variance of (-4x-6)
3- the moment generating function about the origin
solutions :
(1) {e ^(-2t)} * {e^((5e^3t)-5)}
Mr F says: Correct, since if X has moment generating function m(t) then (it can be easily shown that) aX + b has moment generating function . And you have m(t) from question 3.
(2) mean = -26 & variance = 80
Mr F says: Correct, since E(-4X - 6) = -4 E(X) - 6 and Var(-4X - 6) = 16 Var(X).
(3) 30
Mr F says: Wrong. .