A person’s birthday occurs on a day i with probability P i , where i = 1, ..., n. (Of course, P 1 + ... + P 2 = 1.) Assume independent assignment of birthdays among different people. In a room with k people, let P k = P k (p 1 , ..., p n ) be the probability that no two persons share a birthday. Show that this probability is maximized when all birthdays are equally likely: p i = 1/n ∀i.

A person’s birthday occurs on a day i with probability P i , where i = 1, ..., n. (Of course, P 1 + ... + P 2 = 1.) Assume independent assignment of birthdays among different people. In a room with k people, let P k = P k (p 1 , ..., p n ) be the probability that no two persons share a birthday. Show that this probability is maximized when all birthdays are equally likely: p i = 1/n ∀i.

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Description: A person’s birthday occurs on a day i with probability P i , where i = 1, ..., n. (Of course, P 1 + ... + P 2 = 1.) Assume independent assignment of birthdays among different people. In a room with k people, let P k = P k (p 1 , ..., p n ) be the pro

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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