9-15 - Exercise 9-15 Start w/ table w/o information. States...

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Start w/ table w/o information. States are equi-probable P(s i ) = .25 s 1 s 2 s 3 s 4 E(v) One 100 90 30 20 60 Two 30 20 100 90 60 Three 30 150 30 30 60 Four 30 30 30 150 60 Two possible signals—odd or even Odd signal s 1 or s 3 What’s the optimal act choice if we receive odd signal? s 1 s 3 E(v) One 100 30 65 Two 30 100 65 Three 30 30 30 Four 30 30 30 Even signal s 2 or s 4 What’s the optimal act choice if we receive even signal? s 2 s 4 E(v) One 100 20 60 Two 20 90 55 Three 150 30 90 Four 30 150 90 So if the signal is odd, our E(v) is 65. If signal is even, E(v) is 90. So our expected value, when given signal odd or even, is: E(v) = .25(65) + .25(65) + .25(90) + .25 (90) = .50(65) + .50(90) = 77.5 How much would we be willing to pay for this information? The difference between our expected value with no information and the expected value with information E(v) 77.5 EV (no info) 60.0 Willing to pay 17.5 PART C What if we have a high/low signal? Low signal
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9-15 - Exercise 9-15 Start w/ table w/o information. States...

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