Assume you roll two fair, standard dice. Let Xmin and Xmax be the minimum and maximum of the two rolls, respectively. (a) Find the conditional expectation of Xmin given Xmax. (b) Consider E(Xmin|Xmax) as a random variable and find its PMF.
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Since the dice are fair and standard, each outcome has a probability of 1/6. Therefore, we can write: P(Xmax = k) = P(X1 = k or X2 = k) = 1/6 + 1/6 = 1/3, for k = 1, 2, ..., 6 Now, let's consider the possible values of Xmin given Xmax = k. If k = 6, then Xmin Show more…
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