Let X - binomial(n, p) and Y ~ binomial(m, p) be independent. a. Derive the MGF of W = X + Y. b. By the uniqueness property of the MGF, what is the probability distribution of W? c. Find the mean and variance of W using its MGF. C.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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3. Let X - binomial(n, p) and Y ~ binomial(m, p) be independent.
a. Derive the MGF of W = X + Y.
b. By the uniqueness property of the MGF, what is the probability distribution of W?
c. Find the mean and variance of W using its MGF.
Transcribed Image Text:3. Let X - binomial(n, p) and Y ~ binomial(m, p) be independent. a. Derive the MGF of W = X + Y. b. By the uniqueness property of the MGF, what is the probability distribution of W? c. Find the mean and variance of W using its MGF.
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