Let random variables X with mgf Mt06et3104et3 Which is false

Let random variables X with m.g.f. M(t)=(0.6et)3/[1-0.4et]3.  Which is false for X ?  X has a NB(3, 0.6) (negative binomial) distribution  P(X = 3) = 0.216  P(X = 4) = 0.0864  E(X)= 5  Var = 10/3

Solution

From the given MGF it is true that X has a Negative Binomial Distribution with k=3 and p=0.6

Probability distribution function is givenby:

P(X=x) = (x-1)C(3-1) 0.6³ (1-0.6)^x-3

Putting X=3, P(X=3) = 0.216

Putting X=4, P(X=4) = 0.2592

So C is false.