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Consider a deck consisting of seven cards, marked 1, 2, . . ., 7. Three of...

  1. Consider a deck consisting of seven cards, marked 1, 2, . . ., 7. Three of these cards are selected at random. Define an rv W by W 1⁄4 the sum of the resulting numbers, and compute the pmf of W. Then compute E(W) and Var(W). [Hint: Consider outcomes as unordered, so that (1, 3, 7) and (3, 1, 7) are not different outcomes. Then there are 35 outcomes, and they can be listed.] (This type of rv actually arises in connection with Wilcoxon’s rank-sum test, in which there is an x sample and a y sample and W is the sum of the ranks of the x’s in the combined sample.)

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