Solution Found!
Find the moment-generating function for the gamma
Chapter 3, Problem 7E(choose chapter or problem)
Problem 7E
Find the moment-generating function for the gamma distribution with parameters α and θ.
Hint: In the integral representing E(etX ), change variables by letting y = (1 − θt)x/θ, where 1 − θt > 0.
Questions & Answers
QUESTION:
Problem 7E
Find the moment-generating function for the gamma distribution with parameters α and θ.
Hint: In the integral representing E(etX ), change variables by letting y = (1 − θt)x/θ, where 1 − θt > 0.
ANSWER:
Solution 7E
Step1 of 2:
We have A random variable X which follows gamma distribution with parameter
We need to find the moment generating function(mgf) of gamma distribution.
Step2 of 2:
Let “X” be random variable which follows gamma distribution with parameters
That is X G(
)
The probability mass function of binomial distribution is given below
P(X) = ,
Where,
X = random variable
= parameter