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## Homework Statement

Suppose X is a discrete random variable with probability mass function

p

_{X}(x)=1/5, if x=-2,-1,0,1,2

p

_{X}(x)=0, otherwise

Let Y=X

^{2}. Are X and Y independent? Prove using definitions and theorems.

## Homework Equations

## The Attempt at a Solution

The random variables X and Y are independent <=> p

_{X,Y}(x,y)=p

_{X}(x)p

_{Y}(y) for ALL x,y E R

But the trouble here is that we don't have p

_{X,Y}(x,y) and p

_{Y}(y). What can we do?

Thanks for any help!