You consider investing £800 in stocks of the company X for a certain period. There is a possibility for X to merge with Y, in which case you expect your investment to appreciate £300, otherwise you expect it to depreciate £200. Also, rather than investing, you can choose to keep your £800. By using a utility function U(x)=x−−√, and by defining pthe probability that X merges with Y, what is the condition that p must satisfy for your investment to be worthwhile (rounded to two decimal places)?

You consider investing £800 in stocks of the company X for a certain period. There is a possibility for X to merge with Y, in which case you expect your investment to appreciate £300, otherwise you expect it to depreciate £200. Also, rather than investing, you can choose to keep your £800. By using a utility function U(x)=x−−√, and by defining pthe probability that X merges with Y, what is the condition that p must satisfy for your investment to be worthwhile (rounded to two decimal places)?

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...

See similar textbooks

Similar questions

Gabrielle has purchased the 2-year extended warranty from a retailer to cover the value of hers new cellphone in case if it gets damaged or becomes inoperable for the price of $25. Gabrielle's cellphone is worth $1400 and the probability that it gets damaged or becomes inoperable during the length of the extended warranty is estimated to be 4%. Let XX be the retailer's profit from selling the extended warranty. Answer the following questions: 1. Create the probability distribution table for XX : XX outcome profit xx ,$ P(X=x)P(X=x) the cellphone gets damaged or becomes inoperable no claim filed 2. Use the probability distribution table to find the following: E[X]=μX=E[X]=μX= dollars. (Round the answer to 1 decimal place.) SD[X]=σX=SD[X]=σX= dollars. (Round the answer to 1 decimal place.)
%3D . If a and b are constants, then prove that expected value E[aX + b] = aE[X] + b.
An expected utility maximiser owns a car worth £60 000 and has a bank account with £20 000. The money in the bank is safe, but there is a 50% probability that the car will be stolen. The utility of wealth for the agent is u(y) = In(3) and they have no other assets. How much the individual would be willing to pay for a full car insurance, i.e., where the indemnity is equal to the value of the car? A risk-neutral insurance company is willing to insure the car at the premium of = £2/3 for every one pound of coverage. How much insurance coverage will the individual choose to buy? How much profits, in expectation, does the insurance company earn on insuring the individual?
An individual has a vNM utility function over money of u(x) = Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (Make sure to answer in the form, 0.X, i.e. 0.25) Enter your answer here
find Var(X) or o² С. 2. The number of passengers in a car on a freeway has the following probability function: No. of Passengers 2. 4 f(x) a. Find E(X) b. Var(X)
1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
Suppose you have the following joint probability of a stock and a bond having a positive or negative return (negative returns generate zero fees): Stock Positive Return (Y=1) Stock Negative Return (Y=0) Total What is o ? XY a. None of these O b.-0.065 c. -0.0725 d. 0.065 e. 0.0725 Bond Positive Return (X=1) Bond Negative Return (X=0) Total 0.5 0.1 0.6 0.35 0.85 0.05 0.4 0.15 1
A decision maker has a utility function for monetary gains x given by U(x) = (x + 10,000)1/2. (a) Show that the person is indifferent between the status quo and L: With probability 1/3, he or she gains $80,000 With probability 2/3, he or she loses $10,000 (b) Suppose that this person has a painting. If there is a 10% chance that the painting valued at $10,000 will be stolen during the next year, what is the maximum amount (per year) that he/she would be willing to pay for insurance covering the loss of the painting? • What is certainty equivalent? • What is risk premium? (c) Is this person risk-averse, risk-neutral, or risk-taker? Why?
It is equally probable that two signals reach a receiver at any instant of the time T. The receiver will be jammed if the time difference in the reception of the two signals is less than T. Find the probability that the receiver will be jammed.
Cheryl is considering purchasing additional sewing machines to accommodate the increasing demand for her cosplay costumes. Her alternatives are to buy 1 machine, 2 machines, or 3 machines. The profits realized under each alternative are a function of whether her proposal to bid for clothing the official Bandai team is accepted or not. The payoff table below illustrates the profits realized (in $000's) based on the different scenarios Cheryl faces. The probability that her proposal will be accepted is 65%. Alternative Proposal Accepted Proposal Rejected Purchase 1 sewing machine $10 $5 Purchase 2 sewing machines $30 $4 Purchase 3 sewing machines $40 $2 What alternative should Cherly select if she is pessimistic? What alternative should Cherly select based on a criterion of realism with ?α = 0.8?
The manufacturer of a fertilizer guarantees that, with the aid of the fertilizer, 65% of planted seeds will germinate. Suppose the manufacturer is correct. If 9 seeds planted with the fertilizer are randomly selected, what is the probability that more than 6 of them germinate? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.) Continue X S % 5 6 & Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center 8 9 Submit Assignment Accessibility )
A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.2, and P(D) = 0.65 and P(D/B) = 0.25 Find P(B AND D) = Write your answer up to 4 decimal places. 0.0500 is not the answer.