a job, he must immediately decide whether to accept it or decline it and consider the He becomes available. Notice that when considering a new job offer, Joe only knows the relative rank of that job compared to the ones he has already declined. Assume that all n! orderings are equally likely and that once a job is declined it is gone forever. Suppose Joe's strategy is to reject the first k jobs and then accept the first one that is better than all of those first k. For a given value of k, what is the probability that Joe selects the best job? Ii morimize the probability that Joe selects the best job under this strategy?

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6.57 Suppose Joe is seeking a job. He decides to consider n possible jobs. However, after being offered
a job, he must immediately decide whether to accept it or decline it and consider the next job that
becomes available. Notice that when considering a new job offer, Joe only knows the relative rank
of that job compared to the ones he has already declined. Assume that all n! orderings are equally
likely and that once a job is declined it is gone forever. Suppose Joe's strategy is to reject the first k
jobs and then accept the first one that is better than all of those first k.
For a given value of k, what is the probability that Joe selects the best job?
b What value of k would maximize the probability that Joe selects the best job under this strategy?
et Y represent the number of rolls
Transcribed Image Text:6.57 Suppose Joe is seeking a job. He decides to consider n possible jobs. However, after being offered a job, he must immediately decide whether to accept it or decline it and consider the next job that becomes available. Notice that when considering a new job offer, Joe only knows the relative rank of that job compared to the ones he has already declined. Assume that all n! orderings are equally likely and that once a job is declined it is gone forever. Suppose Joe's strategy is to reject the first k jobs and then accept the first one that is better than all of those first k. For a given value of k, what is the probability that Joe selects the best job? b What value of k would maximize the probability that Joe selects the best job under this strategy? et Y represent the number of rolls
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