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Chapter 4: Q. 4.1 (page 173)
Suppose that the random variable is equal to the number of hits obtained by a certain baseball player in his next at-bats. If and, find
The value ofis
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and will take the same -question examination. Each question will be answered correctly by with probability, independently of her results on other questions. Each question will be answered correctly by B with probability , independently both of her results on the other questions and on the performance of
(a) Find the expected number of questions that are answered correctly by both A and B.(b) Find the variance of the number of questions that are answered correctly by either A or B
On a multiple-choice exam with possible answers for each of the questions, what is the probability that a student will get or more correct answers just by guessing?
Repeat Example when the balls are selected with replacement.
In the game of Two-Finger Morra, players show or fingers and simultaneously guess the number of fingers their opponent will show. If only one of the players guesses correctly, he wins an amount (in dollars) equal to the sum of the fingers shown by him and his opponent. If both players guess correctly or if neither guesses correctly, then no money is exchanged. Consider a specified player, and denote by X the amount of money he wins in a single game of Two-Finger Morra.
(a) If each player acts independently of the other, and if each player makes his choice of the number of fingers he will hold up and the number he will guess that his opponent will hold up in such a way that each of the possibilities is equally likely, what are the possible values of and what are their associated probabilities?
(b) Suppose that each player acts independently of the other. If each player decides to hold up the same number of fingers that he guesses his opponent will hold up, and if each player is equally likely to hold up or fingers, what are the possible values of and their associated probabilities?
Four independent flips of a fair coin are made. Let denote the number of heads obtained. Plot the probability mass function of the random variable .
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