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Chapter 4: Q.4.56 (page 167)
How many people are needed so that the probability that at least one of them has the same birthday as you is greater than ?
The probability the same birthday found to be.
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A newsboy purchases papers at cents and sells them at cents. However, he is not allowed to return unsold papers. If his daily demand is a binomial random variable with , approximately how many papers should he purchase so as to maximize his expected profit?
Prove
Hint: Use integration by parts.
In Example , suppose that the department store incurs an additional cost of for each unit of unmet demand. (This type of cost is often referred to as a goodwill cost because the store loses the goodwill of those customers whose demands it cannot meet.) Compute the expected profit when the store stocks units, and determine the value of data-custom-editor="chemistry" that maximizes the expected profit.
Five men and women are ranked according to their scores on an examination. Assume that no two scores are alike and all possible rankings are equally likely. Letdenote the highest ranking achieved by a woman. (For instance, if the top-ranked person is female.) Find
Five distinct numbers are randomly distributed to players numberedthrough Whenever two players compare their numbers, the one with the higher one is declared the winner. Initially, playersand compare their numbers; the winner then compares her number with that of player and so on. Let denote the number of times player is a winner. Find
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