# transforming exponential distribution to uniform

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?

Given a uniform $$U$$ on the interval $$[0,1]$$, $$2U+3$$ is uniform on $$[3,5]$$.
• Oh, I see. So just compose this function with the function used to transform $X$ to $U$ (given by $1 - e^{-X}$) ie. $2(1 - e^{-X}) + 3$? – 0k33 Nov 4 '18 at 23:24