Suppose that X and Y are two random variables with Let Z XY

Suppose that X and Y are two random variables with Let Z = XY. Find the probability mass function of Z (i.e., find P(Z = z) for each z R).

Solution

z=

xy can take values as 2, 3, 4, 6

i.e. pmf of z is

x	y	xy	z	p
1	2	2	2	0.102564
1	3	3	3	0.230769
2	2	4	4	0.205128
2	3	6	6	0.461538
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