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c.) Assume that the utility of n dollars is . Write an expression for the expected utility of the payment, and show that this expression has a finite value.

c.) Assume that the utility of n dollars is . Write an expression for the expected utility of the payment, and show that this expression has a finite value.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 41CT: On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form...
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hand written plz only c part plzz
C please. 4. You are offered the following game to play: a fair coin is tossed until heads turns up for the first time. If this occurs on the first toss you receive 2 dollars, if it occurs on the second toss, you receive = 4 dollars, for %3D and in general, if heads turns up the first time on the nth toss, you receive dollars. a.) Show that the expected value of your winnings does not exist (i.e.,is given by a divergent sum) for this game. Does this mean that this game is favorable no matter how much you pay to play it? b.) Assume that you receive only dollars if any number greater than or equal to ten tosses are required to obtain the first head. Show that your expected value for this modified game is finite and find its value. c.) Assume that the utility of n dollars is . Write an expression for the expected utility of the payment, and show that this expression has a finite value.
Transcribed Image Text:C please. 4. You are offered the following game to play: a fair coin is tossed until heads turns up for the first time. If this occurs on the first toss you receive 2 dollars, if it occurs on the second toss, you receive = 4 dollars, for %3D and in general, if heads turns up the first time on the nth toss, you receive dollars. a.) Show that the expected value of your winnings does not exist (i.e.,is given by a divergent sum) for this game. Does this mean that this game is favorable no matter how much you pay to play it? b.) Assume that you receive only dollars if any number greater than or equal to ten tosses are required to obtain the first head. Show that your expected value for this modified game is finite and find its value. c.) Assume that the utility of n dollars is . Write an expression for the expected utility of the payment, and show that this expression has a finite value.
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