Refer to Exercise 3.145. Use the uniqueness of moment-generating functions to give the distribution of a random variable with moment-generating function m(t) = (.6et + .4)3.

Reference

If Y has a binomial distribution with n trials and probability of success p, show that the moment-generating function for Y is

Solution 149E

Step1 of 2:

Let us consider a random variable ‘Y’ it follows binomial distribution with parameters ‘n and p’.

Also we have moment generating function that is .

We need to give the distribution of a random variable with this moment-generating function.

Step2 of 2:

We know that the moment generating function of binomial distribution is,

The given moment generating function is...