question archive We have two fair three-sided dice, indexed by i=1,2

We have two fair three-sided dice, indexed by i=1,2

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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.

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

 

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