are x and y independent Let the joint PMF of the two discret

are x and y independent?

Let the joint PMF of the two discrete random variables X and Y be given by: for x = 1,2, 3; 6. P(X, Y) = (x + 3y)/K, for x = 1, 2, 3; and y = 1, 2; and 0, otherwise. i) Find K in order for the P(X, Y) to be a joint pmf for X and Y. i) Are X and Y independent? Justify your answer.

Solution

ii)

X and Y are independent if P(x|y) = P(x), for all values of X and Y. From the probability distribution table, we know the following:

P(X=1) = 11/39 ;  P(x=1 | y=1) = (4/39)/(15/39)= 4/15;

Not equal,

hence Not Indipendent