A payoff table is given below with decision alternatives d1, d2, and d3; as well as the states of nature s1, s2, and s3, respectively. State of Nature Decision s1 s2 s3 d1 250 750 500 d2 300 -250 1200 d3 500 500 600 a) What choice should be made by the optimistic decision maker? b) What choice should be made by the conservative decision maker? c) What decision should be made under minimax regret? d) If the probabilities of d1, d2, and d3 are 0.2, 0.5, and 0.3, respectively, then what choice should be made under expected value? e) What is the expected value of perfect information (EVPI)?
Added by Renee S.
Close
Step 1
In this case, the choices would be: - For state of nature s1: d2 with a payoff of 300 - For state of nature s2: d2 with a payoff of 1200 - For state of nature s3: d3 with a payoff of 600 Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 62 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
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 =
Luke H.
A decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table. Decision Alternative | States of Nature --------------------- | ---------------- d1 | 15 10 11 6 d2 | 12 11 9 8 d3 | 10 11 11 12 d4 | 9 11 12 14 The decision maker obtains information that enables the following probability assessments: P(s1) = 0.5, P(s2) = 0.2, P(s3) = 0.2, and P(s4) = 0.1. (a) Use the expected value approach to determine the optimal decision. EV(d1) EV(d2) EV(d3) EV(d4) The optimal decision is d1 d2 d3 d4. (b) Now assume that the entries in the payoff table are costs. Use the expected value approach to determine the optimal decision. The optimal decision is d1 d2 d3 d4.
Sri K.
A decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table. The decision maker obtains information that enables the following probabilities assessments: P(s1) = 0.5, P(s2) = 0.2, P(s3) = 0.2, and P(s4) = 0.1. (a) Use the expected value approach to determine the optimal decision. EV(d1), EV(d2), EV(d3), EV(d4). The optimal decision is. (b) Now assume that the entries in the payoff table are costs. Use the expected value approach to determine the optimal decision. The optimal decision is.
Lucas F.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD