Dear Researchers,
Greetings,
I am wondering how to deal with the following situation.
Let we have two independent and identically (e.g. exponential) distributed random variables X and Y with given PDF and CDF. I fully understand how to find the PDF and CDF of min(X,Y) or max(X,Y). However, if we define another random variable Z=X.Y. How to find the PDF and CDF of min(Z,X) or min(Z,Y).
Using the following link,
https://en.wikipedia.org/wiki/Product_distribution
I have managed to get the close form expression for the PDF of Z given in the attached image (assuming X_1 and X_2 instead of X and Y ).
Many thanks in anticipation.
Waseem Raza