I have random variables A and B, given by Beta distributions. This can be easily defined in Mathematica.
I have a conditional probability P(C|A,B) which I custom-design as a function. The function is a probability distribution of C given each (a,b) as parameter:
$ P(C=c|A=a,B=b) \sim \mbox{Beta distribution of C with mean} = a b $.
The variance of distribution C would be the average of the variances of distributions A and B.
How can I specify this in Mathematica?
Finally, I need to marginalize P(C) via:
$ P(C) = \int_0^1 \int_0^1 P(C|A,B) P(A) P(B) da db $
How can I do that in Mathematica?
