The probability mass function of a pair of discrete random variables (X,Y) is the function f(x,y)=P(X=x,Y=y). The conditional mass function of Y given X is the function f(y|x)=P(Y=y|X=x). Thus the mass function (left-hand plot) computes probabilities of intersections, while the conditional mass function (right-hand plot) computes conditional probabilities. For each x value, the slice through the conditional mass function at that value gives the distribution of Y when X assumes the value x. The mean of this distribution is the conditional expectation of Y given X=x, E[Y|X=x]. The weighted average of the conditional expectations, with the weights given by the probability that X=x, is the expected value of Y.You can reverse the roles of X and Y to obtain the conditional mass function of X given Y and the conditional expectation of X given Y=yEducação Superior::Ciências Exatas e da Terra::Matemática