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 ¼ 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.)

There are possible outcomes. At the least, you can draw (1, 2, 3) to get a sum of 6, and at most (5, 6, 7) for a sum of 18. Then the PMF is

That is, consider all the possible sums and their integer partitions. For example,

6 = 1 + 2 + 3

7 = 1 + 2 + 4

8 = 1 + 2 + 5 = 1 + 3 + 4

9 = 1 + 2 + 6 = 1 + 3 + 5 = 2 + 3 + 4

and so on.

Then the expected value is

We can find the variance via

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

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step-by-step explanation: