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# Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...

Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y.

Let random variable Z be |X-Y|. The range of Z will be from 0 to 3.

1. Find E(Z).

2. Find P(Z = 1|Z <3).

3. What is the probability that you have to play the game 4 times before you roll Z=3?

4. What is the probability that when you play the game 10 times, you get Z=1 6 times out of the 10 rolls?

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