I have this graph B<-A->C and I have the joint probability distribution of A and B , P(A,B), and the joint probability distribution of A and C, P(A,C). I want to compute the average of B and C. my attempt is to sum the expectations and divide by 2 as follows :
$AVG(B,C) = ( E[B] + E[C] ) / 2 $
where 2 is the number of random variables I want to compute the average for. Is this mathematically correct ? or should I multiply the the expectations and divide by 2 ? Note that B is independent of C given A. All the variables are discrete.