J Suppose that X is a random variable with moment geniftjio

?% ?J. Suppose that X is a random variable with moment gen&iftjion; .? ..b.?.??--?J _ .... ; . ??,?-e-_.._I_--____-I___ ? w ?- _- ________ Find P( X 2). M(t) oc e(tj) j! A)O B) I 2e C) e 2 D) i=o j i=o 1 J

Solution

given,

M(t)=sigma((e^(tj-1)/j!) from j=0 to j=inf.

       on solving we get,

M(t)=(e^-1/0!)+(e^(t-1)/1!)+(e^(2t-1)/2!)+(e^(3t-1)/3!)+................

P(X=2)=(e^-1/0!)+(e^(t-1)/1!)+(e^(2t-1)/2!).