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b. Now suppose that George instead considers investing $1,000 apiece in each of the 10 different companies. i. What is George's expected wealth in this case? ii. What is George's expected utility in this case? iii. Is George willing to invest $1,000 apiece in each of the 10 companies?

b. Now suppose that George instead considers investing $1,000 apiece in each of the 10 different companies. i. What is George's expected wealth in this case? ii. What is George's expected utility in this case? iii. Is George willing to invest $1,000 apiece in each of the 10 companies?

A First Course in Probability (10th Edition)
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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1. George's utility function over wealth is U(W) = W1/2 and his current wealth is W = 10,000. George is considering investing his entire wealth in the stock of a pharmaceutical company (or companies) trying to develop a Covid-19 vaccine. (If he does not invest, he simply retains his wealth of $10,000.) Exactly 10 companies are trying to develop a vaccine. Each company has a 0.1 probability of success and a 0.9 probability of failure. If a company succeeds in developing a vaccine, each $1 invested in the company turns into $12.10. If a company fails to develop a successful vaccine, each $1 invested in the company turns into $0. It is certain that exactly one (and only one) company will succeed in developing a vaccine but it is unknown which company that will be. Sunne Ceorso conciders investing all $10 000 in asingle company. i. What is George'scEENndkuAa. i. What is George SeXpected------ UIN The answer is not a round otec nu H. 150Corge wifling to inve 000 m a sīgie company? b. Now suppose that George instead considers investing $1,000 apiece in each of the 10 different companies. i. What is George's expected wealth in this case? ii. What is George's expected utility in this case? iii. Is George willing to invest $1,000 apiece in each of the 10 companies?
Transcribed Image Text:1. George's utility function over wealth is U(W) = W1/2 and his current wealth is W = 10,000. George is considering investing his entire wealth in the stock of a pharmaceutical company (or companies) trying to develop a Covid-19 vaccine. (If he does not invest, he simply retains his wealth of $10,000.) Exactly 10 companies are trying to develop a vaccine. Each company has a 0.1 probability of success and a 0.9 probability of failure. If a company succeeds in developing a vaccine, each $1 invested in the company turns into $12.10. If a company fails to develop a successful vaccine, each $1 invested in the company turns into $0. It is certain that exactly one (and only one) company will succeed in developing a vaccine but it is unknown which company that will be. Sunne Ceorso conciders investing all $10 000 in asingle company. i. What is George'scEENndkuAa. i. What is George SeXpected------ UIN The answer is not a round otec nu H. 150Corge wifling to inve 000 m a sīgie company? b. Now suppose that George instead considers investing $1,000 apiece in each of the 10 different companies. i. What is George's expected wealth in this case? ii. What is George's expected utility in this case? iii. Is George willing to invest $1,000 apiece in each of the 10 companies?
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