If A and B are independent discrete random variables and C = A+B, then how should one compute the pmf of P(A|C)?
For example, let X be the result from a coin toss(1 or 0 for H and T) and Y be the result from a second coin toss.
Then, the combinations are x,y,z = (1,1,2)(0,1,1)(1,0,1)(0,0,0)
Thus P(Y|Z) is: when z = 0, P(Y=1|Z=0) = 0. and P(Y=0|Z=0) = 1 when z = 1, P(Y=1|Z) = 1/2 and when Z=2, P(Y|Z) = 1 and so on
How can this be summarized in to a PMF? and what should be the approach for continuous random variables?