Transforming exponential distribution to uniform

exponential distributionprobabilityprobability distributionsuniform distribution

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?

Best Answer

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