19. You are given the following payoff table with profits (in $). Decision States of Nature Alternative s1 s2 di 1000 3000 d2 4000 500 Assume the following probability information is given, where Iı and I2are the outcomes of the sample information available: P(s1) = 0.45; P(Iı | s1) = 0.7; P(I2 | s1) = 0.3 P(s2) = 0.55; P(lh | s2) = 0.6; P(I2 | s2) = 0.4 (a) [2] Find the values of P(I1) and P(I2). (b) [2] Determine the values of P(s1 | I1), P(s2 I I1), P(s1 | I2), and P(s2 | I2). (c) [4] Determine the optimal strategy based on the sample information I and 2. What is the expected value of your solution?
19. You are given the following payoff table with profits (in $). Decision States of Nature Alternative s1 s2 di 1000 3000 d2 4000 500 Assume the following probability information is given, where Iı and I2are the outcomes of the sample information available: P(s1) = 0.45; P(Iı | s1) = 0.7; P(I2 | s1) = 0.3 P(s2) = 0.55; P(lh | s2) = 0.6; P(I2 | s2) = 0.4 (a) [2] Find the values of P(I1) and P(I2). (b) [2] Determine the values of P(s1 | I1), P(s2 I I1), P(s1 | I2), and P(s2 | I2). (c) [4] Determine the optimal strategy based on the sample information I and 2. What is the expected value of your solution?
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![19. You are given the following payoff table with profits (in $).
Decision
States of Nature
Alternative
s1
s2
di
1000
3000
d2
4000
500
Assume the following probability information is given, where Iı and I2are the
outcomes of the sample information available:
P(s1) = 0.45;
P(Iı | s1) = 0.7;
P(I2 | s1) = 0.3
P(s2) = 0.55;
P(lh | s2) = 0.6;
P(I2 | s2) = 0.4
(a) [2] Find the values of P(I1) and P(I2).
(b) [2] Determine the values of P(s1 | I1), P(s2 I I1), P(s1 | I2), and P(s2 | I2).
(c) [4] Determine the optimal strategy based on the sample information I and 2.
What is the expected value of your solution?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c819c03-7758-4add-8e13-f7df3b89a05b%2F097e9d3f-dd8f-49ed-89a5-f7e1ace7b3db%2Fj0o8tx_processed.png&w=3840&q=75)
Transcribed Image Text:19. You are given the following payoff table with profits (in $).
Decision
States of Nature
Alternative
s1
s2
di
1000
3000
d2
4000
500
Assume the following probability information is given, where Iı and I2are the
outcomes of the sample information available:
P(s1) = 0.45;
P(Iı | s1) = 0.7;
P(I2 | s1) = 0.3
P(s2) = 0.55;
P(lh | s2) = 0.6;
P(I2 | s2) = 0.4
(a) [2] Find the values of P(I1) and P(I2).
(b) [2] Determine the values of P(s1 | I1), P(s2 I I1), P(s1 | I2), and P(s2 | I2).
(c) [4] Determine the optimal strategy based on the sample information I and 2.
What is the expected value of your solution?
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