Expression for the expected utility of the payment

Assignment Help Basic Statistics
Reference no: EM13970278

You are offered the following game to play: a fair coin is tossed until heads turns up for the first time (see Example 6.3). If this occurs on the first toss you receive 2 dollars, if it occurs on the second toss you receive 22 = 4 dollars and, in general, if heads turns up for the first time on the nth toss you receive 2n dollars.

(a) Show that the expected value of your winnings does not exist (i.e., is given by a divergent sum) for this game. Does this mean that this game is favorable no matter how much you pay to play it?

(b) Assume that you only receive 210 dollars if any number greater than or equal to ten tosses are required to obtain the first head. Show that your expected value for this modified game is finite and find its value.

(c) Assume that you pay 10 dollars for each play of the original game. Write a program to simulate 100 plays of the game and see how you do.

(d) Now assume that the utility of n dollars is √n. Write an expression for the expected utility of the payment, and show that this expression has a finite value. Estimate this value. Repeat this exercise for the case that the utility function is log(n).

Reference no: EM13970278

Questions Cloud

When would the accrual method be used, and why : Please select an exclusion from income. Explain the exclusion and its purpose. What do you think the congressional intent was for this exclusion?
Are rental payments for a business tax deductible : Why do you think that mortgage interest and real estate taxes for a personal residence are tax deductible, but rent payments are not? Are rental payments for a business tax deductible?
How the essays relate to the cave metaphor : What we have said about the essays in class. Whether the essays altered your existing viewpoint about an issue. How the essays relate to the "Cave" metaphor that is the central theme of FYS.
Compare the results for males and females : Estimate the number of claims that the company can expect from beneficiaries of these men within a year.
Expression for the expected utility of the payment : Assume that you only receive 210 dollars if any number greater than or equal to ten tosses are required to obtain the first head. Show that your expected value for this modified game is finite and find its value.
Federal tax legislation generally originates in what body : (TCO 11) Kyle, whose wife died in December 2009, filed a joint tax return for 2009. He did NOT remarry, but has continued to maintain his home in which his two dependent children live. What is Kyle's filing status regarding 2012?
Expected total without finding its distribution : Find, as Cardano did, the expected total without finding its distribution - Large prizes were given for large totals with a modest fee to play the game. Explain why this could be done.
Explain the technical issues in layman''s terms. : You will provide a detailed vulnerabilities assessment document, along with some specific recommendations to implement to address the vulnerabilities you have described. This document should be based on the scenario provided.
Is psychology related to sociology : 1. Is psychology related to sociology? Attempt to explain how they are related. In what ways does the subject matter of psychology differ from that of sociology? You must provide sufficient details/explanations in your answer.

Reviews

Write a Review

Basic Statistics Questions & Answers

  Statistics-probability assignment

MATH1550H: Assignment:  Question:  A word is selected at random from the following poem of Persian poet and mathematician Omar Khayyam (1048-1131), translated by English poet Edward Fitzgerald (1808-1883). Find the expected value of the length of th..

  What is the least number

MATH1550H: Assignment:  Question:     what is the least number of applicants that should be interviewed so as to have at least 50% chance of finding one such secretary?

  Determine the value of k

MATH1550H: Assignment:  Question:     Experience shows that X, the number of customers entering a post office during any period of time t, is a random variable the probability mass function of which is of the form

  What is the probability

MATH1550H: Assignment:Questions: (Genetics) What is the probability that at most two of the offspring are aa?

  Binomial distributions

MATH1550H: Assignment:  Questions:  Let’s assume the department of Mathematics of Trent University has 11 faculty members. For i = 0; 1; 2; 3; find pi, the probability that i of them were born on Canada Day using the binomial distributions.

  Caselet on mcdonald’s vs. burger king - waiting time

Caselet on McDonald’s vs. Burger King - Waiting time

  Generate descriptive statistics

Generate descriptive statistics. Create a stem-and-leaf plot of the data and box plot of the data.

  Sampling variability and standard error

Problems on Sampling Variability and Standard Error and Confidence Intervals

  Estimate the population mean

Estimate the population mean

  Conduct a marketing experiment

Conduct a marketing experiment in which students are to taste one of two different brands of soft drink

  Find out the probability

Find out the probability

  Linear programming models

LINEAR PROGRAMMING MODELS

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd