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# Refer to Exercise 3.147. Use the uniqueness of

ISBN: 9780495110811 47

## Solution for problem 150E Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Problem 150E

Problem 150E

Refer to Exercise 3.147. Use the uniqueness of moment-generating functions to give the distribution

of a random variable with moment-generating function

Reference

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

Step-by-Step Solution:

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

Step 2 of 2

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Refer to Exercise 3.147. Use the uniqueness of