Consider a deck consisting of seven cards, marked 1, 2,…,7. Three of these cards are selected at random. Define anrv W by W 5 the sum of the resulting numbers, and computethe pmf of W. Then compute m and s2. [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 actuallyarises in connection with a statistical procedure calledWilcoxon’s rank-sum test, in which there is an x sampleand a y sample and W is the sum of the ranks of the x’s inthe combined sample; see Section 15.2.)

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Chapter1: Combinatorial Analysis
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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 5 the sum of the resulting numbers, and compute
the pmf of W. Then compute m and s2. [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 a statistical procedure called
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; see Section 15.2.)

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