Originally Posted by

**flower3** 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 $\displaystyle {\color{red} e^{bt} \, m(at)}$. 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. $\displaystyle {\color{red}m(t) = e^{5(e^t - 1)}}$.