2. Preferences under uncertaintySuppose Felix is offered the opportunity to take part in one of two gambles. Gamble A pays $100 with probability 0.92, $500 with probability 0.04,and nothing with probability 0.04. Gamble B pays $100 with certainty.Which of the following inequalities reflects a preference for gamble B over gamble A if Felix's utility from earning X dollars is given by U(X)?ⒸU (100) > U(0.92 × 100) + U(0.04 x 500) + U(0.04 x 0)U(100) U(0.92 x 100) + U(0.04 x 500) + U(0.04 x 0)ⒸU(100) > 0.92U (100) +0.04U (500) + 0.040(0)OU(100) <0.927/(100) + 0.047(500) + 0.047(0)Now suppose he is offered a second set of gambles. Gamble C pays $100 with probability 0.44, $500 with probability 0,04, and nothing withprobability 0.52. Gamble D pays $100 with probability 0.52 and nothing with probability 0.48.If Felix's preferences are consistent, he should prefer gamble

Gamble A pays $100 with probability 0.92, $500 with probability 0.04, and nothing with probability…

Answered: 2. Preferences under uncertainty…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose a person is thinking about entering a MarioKart competition at theirlocal videogame store. The competition costs 20 dollars to enter. The competition consists of 10 matches. The person knows that their chance of winning each match is 65% and that each match is independent of the others. The payout for the competition is: WIN ALL 10 Matches: 500 Dollar Prize WIN 9 Matches: 250 Dollar PrizeWIN 8 Matches: 50 Dollar Prize OTHERWISE: Nothing 1) Suppose that this person enters the competition 5 times.What is the probability they break even?(Hint: To break even they would need to win the $50 prize twice and lose the other three times. Use a modified binomial to calculate this probability.)
4. A merchant stocks a certain perishable item. He knows that on any given day, he will have a demand for either 2, 3, or 4 of this items with probabilities 0.1, 0.4 and 0.5 respectively. What is the average daily demand?
E and F are mutually exclusive events. P (E) = 0.91; P(F) =0.42 . Find P (E| F )
(8) X and Y are independent events. P(X)=0.3; P(Y)=0.4. Find (a) P(X and Y) (b) P(X | Y) (c) P(Y | X) (d) P(X or Y)
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Suppose a neighborhood grocery store buys 5 containers of skim milk at the wholesale price of $11 per container and sells it for $22 per container. After the expiration date, unsold milk is removed from the shelves and the grocer receives a credit from the distributor equal to three-fourths of the wholesale price. If the probability distribution of the variable is X and the number of containers sold from this lot is x f(x) 0 1/15 1 2/15 2 2/15 3 3/15 4 4/15 5 3/15 Calculate the expected utility. (Round to two decimal places)
Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities 0.35, 0.15, 0.35, and 0.15, respectively. (a) Calculate E(X) and then E(5 - X). E(X) E(5-X) = (b) Would the repair facility be better off charging a flat fee of $70 or else the amount $ 150 (5-X) The repair facility ---Select--- be better off charging a flat fee of $70 because E ]= 150 (5-X)] ? Note: It is not generally true that : E ( =) = E(Y)
Consider the following game in a game arcade. The probability of winning a game is p and hence loosingthe game is 1 − p. In order to win a prize you are given three choices:• A: win at least once in 6 games;• B: win at least twice in 12 games; and• C: win at least 3 times in 18 games.1. If p = 16 which of A, B, or C should you choose to maximize your probability of winning the prize?You are required to compute the probabilities for each option to justify your answer.2. Using the formulas derived in part (1), write a R-code to compute (not simulate) and plot the probabilityof winning the prize for options A, B, and C for different values of p varying from 0.1 to 0.9 inincrements of 0.1. Summarize your observation.Regarding the plot: i) All three curves should be drawn in the same plot, ii) Make sure that the threecurves are distinguishable (using different line styles, colors, and/or markers), and iii) make sure toadd a legend that identifies the curves for the three different options…

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