Question: Bound for Glory (variance). Exercise 5.14 addressed the probability density function of a crude roulette wheel with values 1 to 60. A bet of a

Bound for Glory (variance). Exercise 5.14 addressed the probability density function of a crude roulette wheel with values 1 to 60. A bet of a dollar pays $10 on a winning spin. Let X represent the payoff on a one-dollar wager. The probability mass function of potential winnings is therefore:

X Probability 0 59/60 10 1/60 The expected value of a one dollar bet μ = ∑xi

· Pr(X = xi

) = [0 ×

(59/60)] + [10 × (1/60)] = 0 + 0.1667 = 0.1667, or slightly less than 17 cents. What is the variance σ² of a payoff?

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