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?
Transforming exponential distribution to uniform
exponential distributionprobabilityprobability distributionsuniform distribution
Best Answer
Given a uniform $U$ on the interval $[0,1]$, $$ 2U+3 $$ is uniform on $[3,5]$.