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Question 1:
Recall the St. Petersburg game. It starts at $2. Toss a coin and if a head appears, the pot doubles. If tails appears, you win the pot at that time and the game ends. So, if you get H, H, H T, you win $16. The payoff table is,
First head on toss:
1
2
3
4
[...]
n
Payoff, x
$2
$4
$8
$16
$32
$2^{n}
Assume that your utility function is .
Question 1A. What is the expected monetary value of the game, and what should you be willing to pay to play this game?
Question 1B. Do these values differ? If so, explain why the do.
Question 1C. What is the risk premium you are willing to pay to avoid the uncertainty of the gamble.
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Discuss what happens to the width of the confidence interval as the confidence level is increased. Does this seem reasonable? Explain.
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