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The question is to find a function that transforms a random variable $X$ that has an exponential distribution given by parameter $\lambda = 1$ such that the function applied to $X$ has a uniform distribution over the interval $[3, 5]$. I'm familiar with transforming variables to the standard uniform distribution, but the modified range is throwing me off. Any suggestions?

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Given a uniform $U$ on the interval $[0,1]$, $$ 2U+3 $$ is uniform on $[3,5]$.

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  • $\begingroup$ Oh, I see. So just compose this function with the function used to transform $X$ to $U$ (given by $1 - e^{-X}$) ie. $2(1 - e^{-X}) + 3$? $\endgroup$ – 0k33 Nov 4 '18 at 23:24

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