Question

Suppose the moment generating function of X is M(t) = z 1 2-et Find E[X2]

Answer 1

The solution is done showing all steps with calculations and required explanations. Hope you can understand and appreciate the work.

Note that, ECx") - MCE) = 2 met lezo So, ECX?) = d? de² MGF : ad at MGF a 2 et de 2- a hate et (2-et)? t (@*-2)² NOW, d² et MORF 11 at 2 at [@t-2)2 - at a (et) (et-2) -et a (-2)² (et-2)" a cet-2) at e* (et-2²-2e ze cet-2) (et-2)" - (2-2)<-2Cet-ze* [e"-234 et ce +2) (et-2) Now, pulting t=0; we get; E(X²) = e (e°+2) L!(3) Ce-2) (1-2) 3 (Aus) =