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.

The random variable with m(t) = (0.6e^t+ 0.4)^3

follows binomial random variable with parameters p= 0.6 and n= 3

Step-by-step explanation:

Given that p + q = 1

q = 1 - p

The general form of moment generating function, MGF, m(t) is given as

m(t) = [pe^t + q]^n for a binomial distribution

Comparing this to the moment-generating function to [0.6e^t + 0.4]^3

These m(t) functions are exactly the same with

p= 0.6,

q = 1 - 0.6

q= 0.4

n= 3.

Thus, the random variable with m(t) = (0.6e^t+ 0.4)^3

follows binomial random variable with parameters p= 0.6 and n= 3