Problem 2. Counting Votes (#Distributions) In a small voting district, Poisson(A) people arrive to vote during a referendum. Each voter votes for the proposal with probability p and against the proposal with probability (1 - p). Assume everyone casts their vote independently. 1. If D is the difference between the number of votes for the proposal and the number of votes against the proposal, determine E(D) and Var(D). 2. Implement a simulation to check your answers.

Problem 2. Counting Votes (#Distributions) In a small voting district, Poisson(A) people arrive to vote during a referendum. Each voter votes for the proposal with probability p and against the proposal with probability (1 - p). Assume everyone casts their vote independently. 1. If D is the difference between the number of votes for the proposal and the number of votes against the proposal, determine E(D) and Var(D). 2. Implement a simulation to check your answers.

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter15: Decision Analysis

Section: Chapter Questions

Problem 16P: Suppose that you are given a decision situation with three possible states of nature: s1, s2, and...

See similar textbooks

Similar questions

1. In a congressional district somewhere in the U.S., a new representative is being elected. The voters all have one-dimensional political views that can be neatly arrayed on a left-right spectrum. We can define the "location" of a citizen's political views in the following way. The citizen with the most extreme left-wing views is said to be at point 0 and the citizen with the most extreme right-wing views is said to be at point 1. If a citizen has views that are to the right of the views of the fraction x of the state's population, that citizen's views are said to be located at point x. There are two candidates for the congressional seat and they are forced to publicly state their own political position simultaneously on the zero-one left-right scale.
Suppose the following data represent the number of persons unemployed for a given number of months in Killeen, Texas. The values in the first column show the number of months unemployed and the values in the second column show the corresponding number of unemployed persons. Let x be a random variable indicating the number of months a randomly selected person is unemployed. Use the data to develop an empirical discrete probability distribution for x. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution. What is the probability that a person is unemployed for two months or less? Unemployed for more than two months? What is the probability that a person is unemployed for more than six months?
Consider the following society: Share of voters 32% 33% 34% First choice a b c Second choice b c a Third choice c a b These are the voters' true preferences. (i) What is the outcome under plurality voting if everyone votes sincerely? (ii) Assuming voters in groups 2 and 3 vote sincerely, could voters in group 1 misreport to get a better outcome? How many in group 1 need to vote this way for it to work? (iii) Assuming voters in groups 1 and 3 vote sincerely, could voters in group 2 misreport to get a better outcome? (iv) Assuming voters in groups 1 and 2 vote sincerely, could voters in group 3 misreport to get a better outcome?
Which of the following describes disjoint events? Select one: a.Planning a picnic: Event that Friday 13th is chosen for a picnic; Event that it rains on the day of the picnic. b.A person's lifestyle choices: Event the person is a smoker; Event the person drinks heavily. c.What party does a voter prefer: Event the voter prefers Labour Party; Event the voter prefers National Party. d.A person's preferences: Event the person likes shopping for clothes; Event the person likes shopping for garden plants.
The most popular method used to calculate VaR is: Group of answer choices B. Parametric VaR D. All three methods are equal in popularity. C. Monte Carlo Analysis A. Historical Simulation
Consider the random experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. a. How many outcomes are possible? b. List the outcomes. c. What is the probability of obtaining a value of 7? d. What is the probability of obtaining a value of 9 or greater?
The correlation of two variables will be Group of answer choices a. Between -1 and +1, inclusive b. Between 0 and +2, inclusive c. Between 0 and +1, inclusive d. Between minus infinity and plus infinity
Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. The prior probabilities are P(s1) = 0.2, P(s2) = 0.5, and P(s3) = 0.3. With sample information I, P(I|s1) = 0.1, P(I|s2) = 0.05, and P(I|s3) = 0.2. Compute the revised (or posterior) probabilities: P(s1|I), P(s2|I), and P(s3|I).
The results are as followed, 70 percent of the people said yes it is for denise and 30 percent said it is not. For Frank 50 percent said yes it is, and 50 percent said that it is not. 1) Present the game results: Include the empirical results recorded in the lab (or use the results provided). Discuss any strategies you adopted or any issues you encountered in the experiment. 2) Solve the game: Represent the game as a matrix or game tree (appropriate to the game at hand) Solve the game according to the assumptions of game theory explain detailing how you did this. 3) Comparison: Compare the empirical results in 2) to your formal solution in 3); Is there any variation between them? Comment on potential reasons for any variation (or lack of variation).
Directons: Answer each of the questions below. 1.Use a real-life example to describe the following allocation methods. Hint: Use family, friends, teams, church, and/or clubs for examples. · Brute Force · Market · Queuing · Random Selection · Tradition · Equal Shares · Need · Planned 2. Explain the Market System. Give an in-depth example of a Market System. 3. Explain the Planned System. Give an in-depth example of a Planned System. 4. Which allocation system do you think is the most productive or the fairest? Explain. 5. Compare and contrast the Market…
A typical control decision would be best characterised as: Select one: O A. Predicting the cost of offering a new course at a university O B. Identifying how many students should be registered to break even C. Determining why the number of students registered was less than anticipated O D. All of the above.
If two returns are positively related to each other, they will have a ________, and if they are negatively related to each other, the ______________. Group of answer choices positive covariance, covariance will be negative positive covariance, standard deviation will be negative negative covariance, covariance will be zero negative covariance, covariance will be positive This type of risk affects a large number of assets, each to a greater or lesser degree. Group of answer choices systematic risk unsystematic risk idiosynchratic risk principle of diversification True/False. The Dividend Discount Model can be applied to firms that do not pay dividends. Group of answer choices True False