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Chapter 4: Q.4.10 (page 173)
An urn containsballs numbered through . If you withdraw balls randomly in sequence, each time replacing the ball selected previously, find
where is the maximum of the chosen numbers.
Hint: First find .
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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
There are two possible causes for a breakdown of a machine. To check the first possibility would cost C1 dollars, and, if that were the cause of the breakdown, the trouble could be repaired at a cost of R1 dollars. Similarly, there are costs C2 and R2 associated with the second possibility. Let p and 1 鈭� p denote, respectively, the probabilities that the breakdown is caused by the first and second possibilities. Under what conditions on p, Ci, Ri, i = 1, 2, should we check the first possible cause of breakdown and then the second, as opposed to reversing the checking order, so as to minimize the expected cost involved in returning the machine to working order?
If you buy a lottery ticket in lotteries, in each of which your chance of winning a prize is role="math" localid="1646465220038" , what is the (approximate) probability that you will win a prize
(a) at least once?
(b) exactly once?
(c) at least twice?
A satellite system consists of components and functions on any given day if at least of the n components function on that day. On a rainy day, each of the components independently functions with probability whereas, on a dry day, each independently functions with probability . If the probability of rain tomorrow is what is the probability that the satellite system will function?
An interviewer is given a list of people she can interview. If the interviewer needs to interview 5 people, and if each person (independently) agrees to be interviewed with probability 2 3 , what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of
(a) 5 people and
(b) 8 people? For part (b), what is the probability that the interviewer will speak to exactly
(c) 6 people and
(d) 7 people on the list?
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