Need a hint with the following problem:
Let and be independent random variables, with probability distribution functions and . Let What is the probability distribution function for ?
Since and are independent, this gives:
Thus, we can obtain by differentiating both sides w/ respect to and using the fundamental theorem of calculus, which gives
Thanks any help!
Interesting, you have the same question as I have!
I'm specifically looking for the case where X is exponentially distributed, and Y follows a normal distribution.
A closed-form solution seems impossible, hence I tried to estimate the pdf of Z.
Via Monte Carlo simulation, it appears that Z=XY, follows again an exponential distribution for z>0.