Solution Found!
Refer to Exercise 3.147. Use the uniqueness of
Chapter 3, Problem 150E(choose chapter or problem)
Refer to Exercise 3.147. Use the uniqueness of moment-generating functions to give the distribution of a random variable with moment-generating function \(m(t)=\frac{.3 e^{t}}{1-.7 e^{t}}\).
Equation Transcription:
Text Transcription:
m(t)=.3e^t over 1-.7e^t
Questions & Answers
QUESTION:
Refer to Exercise 3.147. Use the uniqueness of moment-generating functions to give the distribution of a random variable with moment-generating function \(m(t)=\frac{.3 e^{t}}{1-.7 e^{t}}\).
Equation Transcription:
Text Transcription:
m(t)=.3e^t over 1-.7e^t
ANSWER:
Solution:
Step 1 of 2:
Let Y has a Geometric distribution with probability of success p, and q be the probability of failure
The moment generating function is
m(t) = , where q = 1 - p
We have, m(t) = - (1)
The claim is to give the distribution