Three fair ten-sided dice with faces 0 to 9 are rolled and the results multiplied. What is the expected product, and what is your 90% confidence interval for its median?
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Three fair ten-sided dice have faces 0 to 9, and the three results are multiplied together. (a) What is the expected product? (b) Give a 90% confidence interval for the median of the product and explain your reasoning; it need not be exact. (c) What is the mode of the product, and how does knowing it change your interval? (d) Narrow your interval to a width of 5 and use it as your opening market. The interviewer trades with you for four rounds and you update the market after each one; then work out your profit or loss. (e) What did the trades tell you, and how should you have set those four markets?
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