We wish to sample from the pdf [ f(x)=x mathrm{e}^{-x}, quad x geqslant 0 ] using acceptance-rejection
Question:
We wish to sample from the pdf
\[ f(x)=x \mathrm{e}^{-x}, \quad x \geqslant 0 \]
using acceptance-rejection with the proposal pdf \(g(x)=e^{-x / 2} / 2, x \geqslant 0\).
(a) Find the smallest \(C\) for which \(C g(x) \geqslant f(x)\) for all \(x\).
(b) What is the efficiency of this acceptance-rejection method?
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Related Book For 
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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