We have two fair three-sided dice, indexed by i=1,2. Each die has sides labelled 1, 2, and 3. We roll the two dice independently, one roll for each die. For i=1,2, let the random variable Xi represent the result of the ith die, so that Xi is uniformly distributed over the set {1,2,3}. Define X=X2−X1.

Question

Calculate the numerical values of following probabilities, as well as the expected value and variance of X:

Answer 1

Plz answer...

Answer 2

Calculate the numerical values of following probabilities, as well as the expected value and variance of X:

P(X=0)=
P(X=1)=
P(X=−2)=
P(X=3)=
E[X]=
var(X)=

Let Y=X2.
Calculate the following probabilities:

P(Y=0)=
P(Y=1)=
P(Y=2)=

Answer 3

P(X=0)= 1/3
P(X=1)= 2/9
P(X=−2)= 1/9
P(X=3)= 0
E[X]= 0
var(X)= 4/3

P(Y=0)= 1/3
P(Y=1)= 4/9
P(Y=2)= 0