2 Indifference Curves in Consequence Space(A) If the utility function is v (c) = c2, where c is income, suppose aperson's preference ordering over actions or prospects in a two-stateworld is given by:U(q, G; T, 72) = T, (4) + 7,(6,)+ T2Depict the indifference curves in a diagram with q on the horizontalaxis and c, on the vertical axis (probabilities held constant). Show thateach indifference curve touches the axes and is everywhere bowedtoward the origin.(B) If U = ET,v(c,) and v(.) is a strictly concave function, show that ifthe individual is indifferent between (c, , c2 ) and (c, c) he will strictlyprefer the convex combination (Ac, + (1 – 1)c, rc, + (1 – )C).Hence draw a conclusion about the shape of the indifference curvesin the (c, ) plane.

Given Indifference Curves in Consequence Space

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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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Exercise 3. Let X be a random variable with mean and variance o². For a € R, consider the expectation E((X-a)²). a) Write E((X-a)²) in terms of a, u and o². b) For which value a is E((X - a)²) minimal? c) For the value a from part (b), what is E((X-a)²)?
3. Suppose Chelsea has the following utility function over sure wealth: v (y) = In y (a) Consider the lottery that yields the outcome $2 with probability and the outcome $8 with probability . What is Chelsea's certainty equivalent for this lottery? 2 3* (b) For the lottery in (b), how much would Chelsea pay to have her risk taken away? (c) What is Chelsea's probability premium at $25 for a lottery that could swing her wealth $20 up or down? What about $15 up or down?
1 Events X and Y are such that P(x)=0.35 and P(x or y)=0.80. Given that X and Y are independent and non‐mutually exclusive, determine p(y). Give your finalanswer as a percentage to two decimal places.
Let (X1, X2, X3) be the random outcome of tossing a fair six-faced die three times, and let (Y(1), Y(2), Y(3) be the order statistics from (X1, X2, X3). We have Y(1) = min (X1, X2, X3), Y(3) = max (X1, X2, X3), and Y(1) < Y(2) < Y(3). Find Pr (Y(1) = 3).
Q2) Suppose that X is a continuous random variable with probability distribution £x(x) = ₁ 0≤x≤4 Find the probability distribution of Y = (x - 2)².
Weights (X) of men in a certain age group have a normal distribution with mean ? = 170 pounds and standard deviation ? = 28 pounds. Find each of the following probabilities. (Round all answers to four decimal places.) (a) P(X ≤ 191) = probability the weight of a randomly selected man is less than or equal to 191 pounds. (b) P(X ≤ 156) = probability the weight of a randomly selected man is less than or equal to 156 pounds. (c) P(X > 156) = probability the weight of a randomly selected man is more than 156 pounds
4. An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having pmf 0.9 f(x) = x = 0 x = 1,2,3,4,5,6 where c is a constant. a) Find c. b) Find the expected value of the amount the insurance company must pay.
Let X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of Yn
Which of the following statements are true (no need to justify)?(1) The transformation of a continuous random variable is always a continuous random variable.(2) The distribution of the transformation of a random variable is always the same as that of the original sat-distribution of the univariate.(3) Many random variables can be represented by a uniformly distributed random variableusing if the quantile function of the distribution is known.(4) The accumulation function of several variables is increasing with respect to each variablefunction.(5) The multidimensional accumulation function is determined by its (one-dimensional) marginal distributionwhere from.(6) The marginal distributions of a discrete random vector are discrete distributions.
The probability distribution of the ratings established by the employees on the relationship they have with their supervisors ranges from 1 (poor) to 5 (excellent). Qualification of employee’s relationship with supervisor (x) Supervisor A f (x) Supervisor B f (x) 1 0.05 0.04 2 0.09 0.10 3 0.03 0.12 4 0.42 0.46 5 0.41 0.28 a) What is the expected value (mean) of the securities offered to the rating of supervisor A? b) What is the expected value (mean) of the securities offered to supervisor B's rating? c) Calculate the variance of the values offered to the rating of supervisor A. d) Calculate the standard deviation of the values offered to the rating of supervisor B. e) Compare their satisfaction with supervisor A with that of supervisor B.
For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish

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