Explanation Let X is a nonnegative, integer-valued random variable. By definition, the mean or expected value of X becomes, E ( X ) = ∑ k = 1 ∞ k P ( X = k ) E ( X ) = P ( X = 1 ) + 2 P ( X = 2 ) + 3 P ( X = 3 ) + ...... Note that the probability of every k -value occurs once, then E ( X ) = ∑ k = 1 ∞ P ( X = k ) + P ( X = 2 ) + 2 P ( X = 3 ) + 3 P ( X = 4 ) + ...... The probability that forevery k -value at least 2 occurs once in the remaining sum, then E ( X ) = ∑ k = 1 ∞ P ( X = k ) + ∑ k = 2 ∞ P ( X = k ) + P ( X = 3 ) + 2 P ( X = 4 ) +

An Introduction to Mathematical Statistics and Its Applications (6th Edition)

6th Edition

ISBN: 9780134114217

Author: Richard J. Larsen, Morris L. Marx

Publisher: PEARSON

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Chapter 3.5, Problem 26Q

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To test: To prove that E(X)=∑k=1∞P(X≥k)

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Chapter 3.5, Problem 25Q

Chapter 3.5, Problem 27Q

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Chapter 3 Solutions

An Introduction to Mathematical Statistics and Its Applications (6th Edition)

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To test: To prove that E ( X ) = ∑ k = 1 ∞ P ( X ≥ k )

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Chapter 3 Solutions