Question

What general form of the mass function of a conditional probability distribution for discrete random variables?

Answer 1

Let X and Y be two discrete random variables. The conditional probability mass function of X given Y=y is a function
`p_(X|Y = y) : RR -> [0,1]` such that
`p_(X|Y=y)(x) = P(X=x|Y=y)`
for any `x\in \RR`,
where `P(X=x|Y=y)` is the probability that `X=x`,
given that `Y=y`.