Differentiating with respect to (p) on both sides of the equation [sum_{x=1}^{infty} p(1-p)^{x-1}=1] show that the geometric

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Differentiating with respect to $p$ on both sides of the equation

\[\sum_{x=1}^{\infty} p(1-p)^{x-1}=1\]

show that the geometric distribution

\[f(x)=p(1-p)^{x-1} \quad \text { for } x=1,2,3, \ldots\]

has the mean $1 / p$.

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Probability And Statistics For Engineers

ISBN: 9780134435688

9th Global Edition

Authors: Richard Johnson, Irwin Miller, John Freund

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Question Posted: Apr 21, 2024 05:00 AM

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Differentiating with respect to (p) on both sides of the equation [sum_{x=1}^{infty} p(1-p)^{x-1}=1] show that the geometric

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Probability And Statistics For Engineers

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