Thanks for clarifying and confirming my answer to the covariance problem.

Sorry, I am a little confused as to which problem you are referring when making the comments. I'll do my best to answer your questions.

First, yes, that symbol was supposed to be the gamma function. For the integral with two beta distributions, the problem is: "Let X~Beta(a,b). Find the PDF of Y= (1-X)/X." I made Z= 1-X and found its distribution to be Z~Beta(b,a). Now, I am at finding Y=Z/X in which I stated the current integral with which I am struggling. Again, here it is:

Further, you asked if X and Z are independent... I'm not positive, but I assume so.

Thanks for your help,

*matheagle*!