4 Suppose we are attending a college which has 3000 students. We wish to choose a subset of size 100 from the student body. Let X represent the subset, chosen using the following possible strategies. For which strategies would it be appropriate to assign the uniform distribution to X? If it is appropriate, what probability should we assign to each outcome?


(a) Take the first 100 students who enter the cafeteria to eat lunch.
     Not Appropriate. The selection process is not random. The first 100 students to the cafeteria may have the same schedule and belong to the same class or group of classes.


(b) Ask the Registrar to sort the students by their Social Security number, and then take the first 100 in the resulting list.
     Not Appropriate. Social Security numbers identiy students by State and probably other demographics varialbes thus making this process non-random.


(c) Ask the Registrar for a set of cards, with each card containing the name of exactly one student, and with each student appearing on exactly one card. Throw the cards out of a third-story window, then walk outside and pick up the first 100 cards that you find.
    Not Appropriate. Although this is a random process, X (outcome) will not have a uniformly distributed probabilty. As each card is pick, since there is no replacement, the probably of picking the next card decreases. That is, probabilty of choosing the 1 frst card is 1/3000 but for card 2 it is 1/2999 and for card 100 it is 1/2900.