# A sequence of n job candidates is prepared to interview for a job. We would like to hire the best

## Question:

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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## Step by Step Answer:

**Related Book For**

## Probability And Statistics

**ISBN:** 9780321500465

4th Edition

**Authors:** Morris H. DeGroot, Mark J. Schervish

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