PLEASE SHOW ALL THE WORK THX We are given two independent di

PLEASE SHOW ALL THE WORK! THX!

We are given two independent discrete random variables: X - distributed uniformly on { -1, 0, 1} and Y - uniformly on {1, 2, 3}. Define Z - XY - the product of X and Y. Find the distribution of Z; Find the expectation and variance of Z; Let Z_1, Z_2, hellips be i.i.d. random variables having the same distribution as Z. Using central limit theorem, compute

Solution

xy can take the following values

Pdf of z and mean are shown below

Mean =0 and var(z) = 28/9

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	x	-1	0	1
y
1		-1	0	1
2		-2	0	2
3		-3	0	3