What is the variance of M, var(M). b. Given that the maximum rolled is a 4, what is the probability that one of the rolls was a 2 ?

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Assume you have a typical fair 6-sided die. That is to say, it has sides 1, 2, 3, 4, 5, 6 and each side has probability of 1/6 of occurring. You are to roll the die twice, and record the maximum, M, of the two 6 rolls. If you roll a 2 and a 3 (or a 3 and a 2), then M = 3. If you roll a 4 and a 4, then M = 4. The rolls are independent of each other.

a. What is the variance of M, var(M).

b. Given that the maximum rolled is a 4, what is the probability that one of the rolls was a 2 ?

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