Answer Happy

= = = = Suppose that X, Y are discrete random variables (not necessarily indepen- dent) with joint PMF p(x, y) = P(X = x,Y = y). Show that the marginal PMF px(x) = P(X = x) of X can be obtained from the joint PMF p(x,y) by “summing away” Y. That is, for any given x, px(x) = {p(x,y). = y Hint: Use the Law of Total Probability. One of the sets in your partition will have probability 0.

Note: Similarly, we can also obtain py(y) by “summing away” X, py(y) = {p(x,y). = х Note: In the case of continuous random variables, the marginal PDFs can be found from the joint PDF, however then we must “integrate away” the unwanted random variable, > = fx(x) = {f(x,y)dy fy() = [ f(x,y)dx. roo = oo