# Math Help - Random Variable PMF

1. ## Random Variable PMF

A random variable X with PMF given by

px(x) = {(x^2)/a, x=-3,-2,-1,0,1,2,3,
0 otherwise}

i believe a = 28 and E[X] = 0

am i right in thinking this?

What is the PMF of the random variable Y = (X-E[X])^2?

Use the random variable Y to find Var[X]

2. a=28 and moo is zero, I mean E(X), sry
and the distribution of X is...

P(X=-3)=P(X=3)=9/28

P(X=-2)=P(X=2)=4/28=1/7

P(X=-1)=P(X=1)=1/28

NOW, let

$Y=X^2$

So, P(Y=9)=P(X=-3)+P(X=3)=18/28=9/14

P(Y=4)=P(X=-2)+P(X=2)=2/7

and P(Y=1)=P(X=-1)+P(X=1)=1/14

E(Y)= 9(9/14)+4(2/7)+1(1/14), which better be the variance of X.

3. thank you! makes sense, i understand now!