Answer:
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
Answer: it follows a binomial random variable with parameters p= 0.6 and n=3
Step-by-step explanation:
Let's look at the moment -generating function of a binomial distribution which is given as,
m(t) = [pet+q]n. If we look closely, these moment - generating functions are exactly the same or we can say they are identical to each other, where
p= 0.6, q= 0.4 and n= 3.Thus, the random variable with moment-generating function m(t) = (0.6et+ 0.4)3 follows binomial random variable with parameters p= 0.6 and n= 3
