Joint Distribution Functions/ part3

Joint Probability Distribution

The joint probability distribution of two discrete random variables X and Y is a function whose domain is the set of ordered pairs (x, y) , where x and y are possible values for X and Y, respectively, and whose range is the set of probability values corresponding to the ordered pairs in its domain. This is denoted by pX,Y(x, y) and is defined as

pX,Y(x, y) = P (X = x and Y = y)



The definition of the joint probability distribution can be extended to three or more random variables. In general, the joint probability distribution of the set of discrete random variables X1 , X2, .... , Xn is given by

p ( x1 , x2 , .... , xn ) = P (X1 = x1 and X2 = x2 and .... Xn = xn )

EX. A box has 10 cartons. Two of them contain check prizes, three of them have gift certificates, and the rest are empty. Two cartons will be picked at random from the box.

Let the random variable X be the number of cartons with check prizes drawn, and let the random variable Y be the number of cartons with gift certificates drawn..........