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