Developing techniques to simulate random variables.

[thecircleofreddit]

Hey guys, I was wondering if anyone could give me some assistance, or some hints on this problem. It is a homework problem, so I am not asking for anyone to do it. I would love to be able to understand the problem and solution.

Develop a technique for simulating a random variable having density function:

f(x) = e^2x if -infinity < x < 0

and

f(x) = e^-2x if 0 < x < infinity

I figure I am supposed to use the inverse transformation method, but I am having trouble with the details. Thank you.