The following payoff table shows profit for a decision...

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.DecisionAlternativeStates of Nature s1s2s3d12409015d2909065The probabilities for the states of nature are P(s1) = 0.65, P(s2) = 0.15, and P(s3) = 0.20.(a)What is the optimal decision strategy if perfect information were available?If s1 then ---Select--- d₁ d₂ d₁ or d₂ ; If s2 then ---Select--- d₁ d₂ d₁ or d₂ ; If s3 then ---Select--- d₁ d₂ d₁ or d₂ .(b)What is the expected value for the decision strategy developed in part (a)?(c)Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?The recommended decision without perfect information is ---Select--- d₁ d₂ d₁ or d₂ .EV = (d)What is the expected value of perfect information?EVPI =

Transcript

00:01 So for this ap statistics problem, we're looking at a payoff table that shows profit for a decision analysis problem with three possible decisions, two decisions, and three possible states of nature.

00:15 We're going to look at parts a, b, and c and solve these one by one.

00:19 And part a is having us look at what is the optimal decision strategy if perfect information were readily available to us.

00:29 So for part a, in order to determine this optimal decision strategy, if this perfect information was available, we first need to calculate the expected payoff for each decision alternative for each state of nature, two by three, and select the decision alternative with the highest expected payoff for each state.

00:58 So bear with me through this.

01:00 We're going to go through this one by one.

01:02 So for starters, we're going to look at decision one and decision two.

01:08 Let's do e, d1, and let's do e, d2.

01:16 So for e, d1, we're going to do, based off of the information given, we're going to do 0 .65 times 24 plus 0 .15 times 9 plus 0 .2 times 9, which is going to come out to this.

01:39 One moment.

01:42 So i'm just going to write this out.

01:44 0 .65 times 24 is 0 .15 times 9 is 0 .2 times 9.

02:07 And this is going to come out to, when you add it all up, 18 .75.

02:13 Okay, that's the expected payoff for decision one.

02:17 E for expected and then d, d1, decision one.

02:20 So now let's do the expected payoff for decision two.

02:23 So we're going to do 0 .65 times 9 plus 0 .15 times 6 plus 0 .2 times 5.

02:53 Make that a little bit more clear for you.

02:55 That is a 5.

03:00 And when you do the whole math, that's going to come out to 7 .75 for the expected payoff for decision two.

03:08 So now we're going to compare these.

03:11 Clearly, the expected payoff for decision one, 18 .75, is greater than 7 .75 for e, d2.

03:18 And so therefore, the optimal decision strategy, if perfect information were available, is to choose this decision one if the state of nature is s1 or s2, and choose decision two if the state of nature is s3.

03:51 So that's what you would choose based off the state of nature...

Question

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