7. A woman has 5 years to find a husband. In year 0, she goes out...

 

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7. A woman has 5 years to find a husband. In year 0, she goes out and finds a man who asks for her hand. Let xo be the quality of the suitor. If she accepts the marriage proposal, then the problem ends. If she rejects the marriage proposal, then she has to wait until next year to find anotherman. Let x₁ be the quality of the man who proposes marriage to her in year 1. If she accepts the marriage proposal, then the problem ends. Otherwise, she has to wait one more year to receive a marriage proposal in year 2... Let Xt, t = 0, ..., 4, be the quality of the man who makes the marriage proposal in year t. Suppose that Xt, t = 0, 4, are independent random variables drawn from the uniform distribution on the unit interval [0, 1], and that the uncertainty concerning x is only resolved in year t. *** Let St, t=0, ..., 4, denote the reservation quality for the suitor in year t. That is, & is the critical qual- ity in year t such that the woman only accepts the marriage proposal in that year if the quality of the suitor is at least . Otherwise, if x < t, then the suitor in year t whose quality is x will be rejected, and the woman will wait for the following year in the hope of finding a better suitor. Find the sequence of reservation qualities &t, t=0, ..., 4. 7. A woman has 5 years to find a husband. In year 0, she goes out and finds a man who asks for her hand. Let xo be the quality of the suitor. If she accepts the marriage proposal, then the problem ends. If she rejects the marriage proposal, then she has to wait until next year to find anotherman. Let x₁ be the quality of the man who proposes marriage to her in year 1. If she accepts the marriage proposal, then the problem ends. Otherwise, she has to wait one more year to receive a marriage proposal in year 2... Let Xt, t = 0, ..., 4, be the quality of the man who makes the marriage proposal in year t. Suppose that Xt, t = 0, 4, are independent random variables drawn from the uniform distribution on the unit interval [0, 1], and that the uncertainty concerning x is only resolved in year t. *** Let St, t=0, ..., 4, denote the reservation quality for the suitor in year t. That is, & is the critical qual- ity in year t such that the woman only accepts the marriage proposal in that year if the quality of the suitor is at least . Otherwise, if x < t, then the suitor in year t whose quality is x will be rejected, and the woman will wait for the following year in the hope of finding a better suitor. Find the sequence of reservation qualities &t, t=0, ..., 4.

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To find the sequence of reservation qualities St we need to determine the threshold values at which ... View the full answer