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 correct is answer is a 9-sided polygon!

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.