If X is a negative binomial rv, then the rv Y = X r is the

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If X is a negative binomial rv, then the rv Y = X − r is the total number of failures preceding the rth success.
a. Use an argument similar to the one presented in this section to derive the pmf of Y.

b. Obtain the mgf of Y.

c. Determine the mean and variance of Y. Are these intuitively consistent with the expressions for E(X) and V(X)? Explain.

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Modern Mathematical Statistics With Applications

ISBN: 9783030551551

3rd Edition

Authors: Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton

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Question Posted: Aug 20, 2023 06:29 AM

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If X is a negative binomial rv, then the rv Y = X r is the

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a Deriving the PMF of Y Recall that the negative binomial random variable X represents the number of ...View the full answer

Modern Mathematical Statistics With Applications

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