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Boris and Natasha agree to play the following game. They will flip a (fair) coin 5...

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Advance Math

Boris and Natasha agree to play thefollowing game. They will flip a (fair) coin 5 times in a row. Theywill compute S = (number of heads H – number of tails T).

a) Boris will pay Natasha S. GraphNatasha’s payoff as a function of S. What is the expected value ofS?

b) How much should Natasha be willingto pay Boris to play this game? After paying this amount, what isher best case and worst case outcome?

This time, after 5 flips of the coin,if there are more heads H than tails T, Boris will pay Natasha H –T. If there are more tails T than heads H, Boris will pay Natashanothing.

c) Graph Natasha’s payoff as afunction of S = H – T. What does this graph remind you of?

d) What is the expected value ofNatasha’s payoff? How much should she be willing to pay to playthis game? After paying this amount, what is her best case andworst case outcome?

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