1. Math
  2. Statistics And Probability
  3. 4 boris and natasha agree to play the following game...

Question: 4 boris and natasha agree to play the following game...

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

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

b) How much should Natasha be willing to pay Boris to play this game? After paying this amount, what is her 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 Natasha nothing.

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

d) What is the expected value of Natasha’s payoff? How much should she be willing to pay to play this game? After paying this amount, what is her best case and worst case outcome?

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