Question

PROBLEM 11.1 (pg 127, #68) An electronics store has 12 of the most recent iphone model in stock. Since silver is the most popular color, 9 of these in stock are silver. Suppose the display case is designed to showcase 7 iphones. Thus, 7 iphones are randomly selected from the current stock. Let X = the number of silver iphones to be displayed. a. The random variable X has a hypergeometric distribution with parameters n = M = , and N= b. What values for X are possible? c. Find PCX > 5) d. Find P(X = 3) e. Determine E[X] or the expected number of silver iphones to be displayed. f. Determine Var[X].

Answer 1

a) n = 7, M = 9, N = 12

b) X = 0, 1, 2, 3, 4, 5, 6, 7

c) P(X > 5) = (9C6 * 3C1 + 9C7)/12C7 = 0.3636

d) P(X = 3) = 0

e) E(X) = n * M/N = 7 * 9/12 = 5.25

f) Var(X) = n * M * (N - M) * (N - n)/(N2(N - 1))

= 7 * 9 * (12 - 9) * (12 - 7)/((12)2(12 - 1))

= 0.59659