States of Nature 19-7. The probabilities assessed with the states of nature in t

Question

States of Nature

19-7. The probabilities assessed with the states of nature in the previous problem are

P(S1)= 0.1, P(S2)= 0.2, P(S3) =0.4, P(S4)= 0.3

Using these probabilities, determine which alternative to select using the expected-value criterion.

Answer: fil in the blank:

Refer to problem 19.7.
The expected payoff under alternative A1 is________ , the expected payoff under A2 is __________ , the expected payoff under A3 is___________ , and the expected payoff under A4 is ___________ ; therefore, the expected value criterion (strategy) tells us to choose action ______________ (enter either A1, A2, A3, or A4).

S1 S2 S3 S4 A1 170 45 -60 100 A2 30 190 175 -65 A3 145 -50 120 110 A4 -40 80 10 70

Explanation / Answer

P(S1)= 0.1, P(S2)= 0.2, P(S3) =0.4, P(S4)= 0.3

expected payoff under alternative A1 is=170*0.1+ 45*0.2 - 60*0.4 +100*0.3=32

expected payoff under alternative A2 is=30*0.1+ 190*0.2 +175*0.4 -65*0.3=91.5

expected payoff under alternative A3 is=145*0.1 -50*0.2 +120*0.4 +110*0.3= 85.5

expected payoff under alternative A4 is= -40*0.1+ 80*0.2 +10*0.4 +70*0.3=37

therefore, the expected value criterion (strategy) tells us to choose action A2_

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