Find an appropriate function phi, so that if U is uniform on the interval (0,1), then phi(U) is exponential with rate 1

Question

I'm not sure what the question is asking for. The cdf? Help would be greatly appreciated

Answer 1

Hint: This is a conceptual question. If you've taken a simulation class the answer will be apparent if you recall how to generate random variables.

If you have a continuous, real-valued random variable, $X$ with density function $f(x)$, then $F(x):=\int_0^x f(x) dx$ gives us a function that maps values from the domain of $X$ to the interval $[0,1]$.

Now, the question wants you to find a function that when fed values from a standard uniform random variable generates values from and exponential distribution with rate 1.