HW4Solutions (dragged) 6

# HW4Solutions (dragged) 6 - and P(4 = 1 4 Thus the optimal...

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that the best prize is selected is P ( r ) = n X i =1 P (prize i is selected | prize i is the best) P (prize i is the best) = r - 1 X i =1 0 · 1 n + n X i = r P (best prize among first i - 1 is among first r - 1 | prize i is the best) · 1 n = n X i = r r - 1 i - 1 1 n = r - 1 n n X i = r 1 i - 1 When n = 4, r can take on 2, 3, and 4. P (2) = 11 / 24 , P (3) = 5 /
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Unformatted text preview: and P (4) = 1 / 4. Thus, the optimal strategy is to reject the frst prize and take the frst subsequent prize that is better than the frst prize. The probability oF success is 11 / 24. 6...
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