Question

Suppose that X is a random variable with MGF Mx(t) = (1/8)e^t + (l/4)e^t2 + (5/8)e^t5. a)What is the distribution of X?

b)What is P[X = 2]?

Answer 1

Since $MGF = E(e^{tX}) = \sum[ P(X=k) \times e^{tk} ]$ , we compare terms to get the PMF:

P(X=1) = 1/8

P(X = 2) = 1/4

P(X = 5) = 5/8

and P(X= x) = 0 for other values.

Thus, P(X=2) = 1/4 = 0.25