Explanation Given information: X is a geometric random variable with parameter p . Explanation: A random variable X is a geometric random variable with parameter p . The general formula for the expected value is E ( x ) = ∑ x = 0 x Pr ( X = x ) A random variable X follows geometric distribution, hence Pr ( X = x ) = p x ( 1 − p ) Thus, E ( x ) = 0 ⋅ Pr ( X = 0 ) + 1 ⋅ Pr ( X = 1 ) + 2 ⋅ Pr ( X = 2 ) + 3 ⋅ Pr ( X = 3 ) + ... = p ( 1 − p ) + 2 p 2 ( 1 − p ) + 3 p 3 ( 1 − p ) + ... = p ( 1 − p ) [ 1 + 2 p + 3 p 2 +

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 12.5, Problem 21E

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The formula for E(X) by using the power series formula, where X is a geometric random variable with parameter p.

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Chapter 12.5, Problem 20E

Chapter 12.5, Problem 22E

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Chapter 12 Solutions

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The formula for E ( X ) by using the power series formula, where X is a geometric random variable with parameter p .

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The formula for E(X) by using the power series formula, where X is a geometric random variable with parameter p.

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Chapter 12 Solutions