2. Let the following lotteries: L has prizes (0, 2, 4, 6) with equal probabilities. L' has prizes (0.1, 3, 5.9) with equal probabilities. (a) Compute the expected values of the two lotteries and verify they are the same. (b) Compute the variances of the two lotteries and verify that the second lottery has a bigger variance. (c) One would be tempted to conclude that L second order stochastically dominates L', that is, any risk averse decision maker would prefer L over L'. Not true, unfor- tunately. Consider a decision maker with the following Bernoulli utility function u(x) = = 2x 3+x if x ≤ 3 if x > 3 Verify that the decision maker is risk averse and that the decision maker prefers L' over L.
2. Let the following lotteries: L has prizes (0, 2, 4, 6) with equal probabilities. L' has prizes (0.1, 3, 5.9) with equal probabilities. (a) Compute the expected values of the two lotteries and verify they are the same. (b) Compute the variances of the two lotteries and verify that the second lottery has a bigger variance. (c) One would be tempted to conclude that L second order stochastically dominates L', that is, any risk averse decision maker would prefer L over L'. Not true, unfor- tunately. Consider a decision maker with the following Bernoulli utility function u(x) = = 2x 3+x if x ≤ 3 if x > 3 Verify that the decision maker is risk averse and that the decision maker prefers L' over L.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:2. Let the following lotteries: L has prizes (0, 2, 4, 6) with equal probabilities. L' has prizes
(0.1, 3, 5.9) with equal probabilities.
(a) Compute the expected values of the two lotteries and verify they are the same.
(b) Compute the variances of the two lotteries and verify that the second lottery has a
bigger variance.
(c) One would be tempted to conclude that L second order stochastically dominates
L', that is, any risk averse decision maker would prefer L over L'. Not true, unfor-
tunately. Consider a decision maker with the following Bernoulli utility function
u(x) =
2x
3 + x
if x ≤ 3
if x > 3
Verify that the decision maker is risk averse and that the decision maker prefers L'
over L.
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