Let (X sim operatorname{Gamma}(alpha, lambda)). Show that the pdf of (Z=1 / X) is equal to [

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Let $X \sim \operatorname{Gamma}(\alpha, \lambda)$. Show that the pdf of $Z=1 / X$ is equal to

\[ \frac{\lambda^{\alpha}(z)^{-\alpha-1} \mathrm{e}^{-\lambda(z)-1}}{\Gamma(\alpha)}, \quad z>0 \]

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Data Science And Machine Learning Mathematical And Statistical Methods

ISBN: 9781118710852

1st Edition

Authors: Dirk P. Kroese, Thomas Taimre, Radislav Vaisman, Zdravko Botev

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Question Posted: May 19, 2024 02:03 AM

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Let (X sim operatorname{Gamma}(alpha, lambda)). Show that the pdf of (Z=1 / X) is equal to [

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Data Science And Machine Learning Mathematical And Statistical Methods

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