Question

1. You are given the following payoff table with profits (in $).

Decision Alternative	States of Nature
	s1	s2
d1	1000	3000
d2	4000	500

Assume the following probability information is given, where I1 and I2 are the outcomes of the sample information available:

P(s1) = 0.45;	P(I1 | s1) = 0.7;	P(I2 | s1) = 0.3
P(s2) = 0.55;	P(I1 | s2) = 0.6;	P(I2 | s2) = 0.4

1. [2] Find the values of P(I1) and P(I2).

2. [2] Determine the values of P(s1 | I1), P(s2 | I1), P(s1 | I2), and P(s2 | I2).

[4] Determine the optimal strategy based on the sample information I1 and I2. What is the expected value of your solution?

Answer 1

2) The value of P(I1) is

The value of P(I2) is

3)

4) We draw the following tree for the ease of understanding

Moving from the right to the left

chance node 4:

The expected value of node 4 is

chance node 5:

The expected value of node 5 is

chance node 6:

The expected value of node 6 is

chance node 7:

The expected value of node 7 is

Decision node 2:

Choose from 2 options

• d1: with an expected value of $2023.2
• d2: with an expected value of $2209.4

Since this is a payoff table for profits, the optimum decision is the alternative which maximizes the payoff.

The optimum decision for node 2 is d2

ans: The optimum strategy based on sample information I1 is d2

Decision node 3:

Choose from 2 options

• d1: with an expected value of $2239.4
• d2: with an expected value of $1831.05

Since this is a payoff table for profits, the optimum decision is the alternative which maximizes the payoff.

The optimum decision for node 3 is d1

ans: The optimum strategy based on sample information I2 is d1

The expected value at node 1 is

ans: the expected value of your solution is $2220.05