A sequence of n job candidates is prepared to interview for a job. We would like to hire the best
a. Let i >r. Find the probability that the candidate who is relatively the best among the first i interviewed appears in the first r interviews.
b. Prove that Pr(A|Bi) = 0 for i ≤ r and Pr(A|Bi) = r/(i − 1) for i > r.
c. For fixed r, let pr be the probability of A using that value of r. Prove that pr
d. Let qr = pr − pr−1 for r = 1, . . . , n − 1, and prove that qr is a strictly decreasing function of r.
e. Show that a value of r that maximizes pr is the last r such that qr > 0. (Write pr = p0 + q1 + . . . + qr for r > 0.)
f. For n = 10, find the value of r that maximizes pr, and find the corresponding pr value.
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Question Posted: November 25, 2015 03:13:14