SOLUTION: Consider a random variable X whose moments are defined by E[Xn]=n!. Then, M(t)= a) 1/(1-t) b) t/(1-t) c) t/(1-t!) d) None of these

Question 1042953: Consider a random variable X whose moments are defined by E[Xn]=n!. Then, M(t)=
a) 1/(1-t)
b) t/(1-t)
c) t/(1-t!)
d) None of these

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The moment generating function for X (M(t)) is defined for this problem as
:
M(t) = summation from 0 to infinity of (E(x^n) / n!) * t^n
:
M(t) = summation from 0 to infinity of (n! / n!) * t^n
:
M(t) = summation from 0 to infinity of t^n
:
therefore
:
*****************
answer is a)
M(t) = 1 / (1 - t)
*****************
:

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