Frankie and Johnny play the following game. Frankie selects a number at random from the interval [a,

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Frankie and Johnny play the following game. Frankie selects a number at random from the interval [a, b]. Johnny, not knowing Frankie’s number, is to pick a second number from that same interval and pay Frankie an amount, W, equal to the squared difference between the two [so 0 ≤ W ≤ (b − a)2]. What should be Johnny’s strategy if he wants to minimize his expected loss?

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