Could anyone please assist with this problem:
Given $Y$ has an exponential distribution with mean $5$, and $h(y) = exp(-Y)$, find $\mathbb{E}[h(y)]$
2026-03-24 22:01:28.1774389688
expected value of an exponential function of an exponential distribution
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The density of $Y$ is given by $$ f_{Y}(y)=\frac{1}{5}e^{-y/5};\quad (y>0) $$ whence $$ Ee^{-Y}=\int_{0}^\infty \frac{1}{5}e^{-y/5} e^{-y}\,dy $$ which you can compute.