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We'll roll a 6-sided die with an oddly weighted weight in this game. You will either gain (or lose) money depending on the outcome. Die

We'll roll a 6-sided die with an oddly weighted weight in this game. You will either gain (or lose) money depending on the outcome.

Die Number = DN, Probability = P, Winnings = W, the dice number's stats are to their right

DN 1 P 1/6 W win $1

DN 2 P 1/20 W win $20

DN 3 P sqrt(2)/10 W lose $5

DN 4 P 0 W win $10 billion

DN 5 P 1/2 W win $2

DN 6 P (17 - 6*sqrt(2))/60 W win $0

a. What is your expected amount of money that you gain?

b. What is the variance on your winnings? No need to simplify your answer.

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