Determine the evpi for both chance events e and f

Assignment Help Basic Statistics

Reference no: EM13907202

1. (a) Solve the decision tree shown below.

1088_Decision Tree.png

(b) Create risk profiles and cumulative risk profiles for all possible strategies. Is one strategy stochastically dominant? Explain.

2. For the decision tree shown below:

2126_Decision Tree_1.png

(a) Determine the EVPI for chance event E only.

(b) Determine the EVPI for chance event F only.

(c) Determine the EVPI for both chance events E and F: that is, perfect information for both E and F is available before the decision is made.

(d) Do a sensitivity analysis on the probabilities for chance event F and explain/interpret your result.

3. A decision maker faces a risky gamble in which he/she may obtain one of five outcomes. The outcomes are labeled A, B, C, D, and E. Outcome A is the most preferred, and E is the least preferred. He/she has made the following three assessments:

(a) He/she is indifferent between having C for sure or a lottery in which he/she wins A with probability 0.5 or E with probability 0.5.

(b) He/she is indifferent between having B for sure or a lottery in which he/she wins A with probability 0.4 or C with probability 0.6.

1. A 50% chance at B and a 50% chance at D.

2. A 50% chance at A and a 50% chance at E.

What are U(A), U(B), U(C), U(D), U(E)?

4. Consider the following gamble:

Win $10 with probability 0.5

Win $40 with probability 0.5

(a) Using the above gamble, show that the logarithmic utility function, U(x) = ln (x), demonstrates decreasing risk aversion.

(b) Using the same reference gamble and a risk tolerance of $35, show that the exponential utility function, U(x) 1 - exp (-x/R), demonstrates constant risk aversion.

Reference no: EM13907202

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