Fundamentals of Statistics (5th Edition)
Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 6.2, Problem 30AYU

In Problems 29–34, (a) construct a binomial probability distribution with the given parameters; (b) compute the mean and standard deviation of the random variable using the methods of Section 6.1; (c) compute the mean and standard deviation, using the methods of this section; and (d) draw a graph of the probability distribution and comment on its shape.

30. n = 8, p = 0.5

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Problem 3. Pricing a multi-stock option the Margrabe formula The purpose of this problem is to price a swap option in a 2-stock model, similarly as what we did in the example in the lectures. We consider a two-dimensional Brownian motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices are modeled by the following equations: dX = dY₁ = X₁ (rdt+ rdt+0₁dW!) (²)), Y₁ (rdt+dW+0zdW!"), with Xo xo and Yo =yo. This corresponds to the multi-stock model studied in class, but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure P is already the risk-neutral measure (Both stocks have rate of return r). We write σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to exchange one share of X for one share of Y. That is, the option has payoff F=(Yr-XT). (a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for the process Xt. Reminder before proceeding to question (b): Girsanov's theorem…
Problem 1. Multi-stock model We consider a 2-stock model similar to the one studied in class. Namely, we consider = S(1) S(2) = S(¹) exp (σ1B(1) + (M1 - 0/1 ) S(²) exp (02B(2) + (H₂- M2 where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with t≥0 Cov (B(¹), B(2)) = p min{t, s}. " The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian motion (W+)+20 (W(1), W(2))+20 such that = S(1) S(2) = = S(¹) exp (011W(¹) + (μ₁ - 01/1) t) 롱) S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t). where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p). Hint: The constants will follow the formulas developed in the lectures. (a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2) functions of (B(1), B(²)). as (b) Using the formulas obtained in (a), show that the process (WA) is actually a 2- dimensional standard Brownian motion (i.e. show that each component is normal, with mean 0, variance t, and that their…
The scores of 8 students on the midterm exam and final exam were as follows.   Student Midterm Final Anderson 98 89 Bailey 88 74 Cruz 87 97 DeSana 85 79 Erickson 85 94 Francis 83 71 Gray 74 98 Harris 70 91   Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary. Test statistic: rs =

Chapter 6 Solutions

Fundamentals of Statistics (5th Edition)

Ch. 6.1 - In Problems 914, determine whether the...Ch. 6.1 - In Problems 914, determine whether the...Ch. 6.1 - In Problems 914, determine whether the...Ch. 6.1 - In Problems 914, determine whether the...Ch. 6.1 - In Problems 15 and 16, determine the required...Ch. 6.1 - In Problems 15 and 16, determine the required...Ch. 6.1 - NW Televisions In the Sullivan Statistics Survey...Ch. 6.1 - Marriage In the following probability...Ch. 6.1 - Ichiros Hit Parade In the 2004 baseball season,...Ch. 6.1 - Waiting in Line A Wendys manager performed a study...Ch. 6.1 - In Problems 21 and 22, (a) construct a discrete...Ch. 6.1 - In Problems 21 and 22, (a) construct a discrete...Ch. 6.1 - Number of Births The graph of the discrete...Ch. 6.1 - Rental Units The graph of the discrete probability...Ch. 6.1 - NW Life Insurance A life insurance company sells a...Ch. 6.1 - Life Insurance A life insurance company sells a...Ch. 6.1 - Blackjack Blackjack is a popular casino game in...Ch. 6.1 - Investment An investment counselor calls with a...Ch. 6.1 - Roulette In the game of roulette, a player can...Ch. 6.1 - Connecticut Lottery In the Cash Five Lottery in...Ch. 6.1 - Powerball Powerball is a multistate lottery. The...Ch. 6.1 - SAT Test Penalty Some standardized tests, such as...Ch. 6.1 - Putting It Together: Sullivan Statistics Survey I...Ch. 6.1 - Prob. 36AYUCh. 6.2 - A binomial experiment is performed a fixed number...Ch. 6.2 - For each trial of a binomial experiment, there are...Ch. 6.2 - True or False: In the binomial probability...Ch. 6.2 - The phrase no more than is represented by the math...Ch. 6.2 - The expected number of successes in a binomial...Ch. 6.2 - As a rule of thumb, if _____, the probability...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 716, determine which of the following...Ch. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - Prob. 24AYUCh. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - Prob. 26AYUCh. 6.2 - Prob. 27AYUCh. 6.2 - In Problems 1728, a binomial probability...Ch. 6.2 - In Problems 2934, (a) construct a binomial...Ch. 6.2 - In Problems 2934, (a) construct a binomial...Ch. 6.2 - In Problems 2934, (a) construct a binomial...Ch. 6.2 - In Problems 2934, (a) construct a binomial...Ch. 6.2 - In Problems 2934, (a) construct a binomial...Ch. 6.2 - In Problems 2934, (a) construct a binomial...Ch. 6.2 - NW On-Time Flights According to flightstats.com,...Ch. 6.2 - Morality In a recent poll, the Gallup Organization...Ch. 6.2 - Toilet Flushing In the Healthy Handwashing Survey...Ch. 6.2 - Allergy Sufferers Clarinex-D is a medication whose...Ch. 6.2 - Sneeze According to a study done by Nick Wilson of...Ch. 6.2 - Sneeze Revisited According to a study done by Nick...Ch. 6.2 - Jury Selection Twelve jurors are randomly selected...Ch. 6.2 - Sullivan Survey: Car Color According to paint...Ch. 6.2 - NW On-Time Flights According to flightstats.com,...Ch. 6.2 - Morality In a recent poll, the Gallup Organization...Ch. 6.2 - Toilet Flushing In the Healthy Handwashing Survey...Ch. 6.2 - Prob. 46AYUCh. 6.2 - Spanking In March 1995, The Harris Poll reported...Ch. 6.2 - Government Solutions? In May, 2000, the Gallup...Ch. 6.2 - Racial Profiling in New York City The following...Ch. 6.2 - Overbooking Flights Historically, the probability...Ch. 6.2 - Athletics Participation According to the High...Ch. 6.2 - Putting It Together: Beating the Stock Market One...Ch. 6.2 - State the criteria for a binomial probability...Ch. 6.2 - Explain what success means in a binomial...Ch. 6.2 - Explain how the value of n, the number of trials...Ch. 6.2 - Prob. 57AYUCh. 6.2 - When can the Empirical Rule be used to identify...Ch. 6 - Determine whether the random variable is discrete...Ch. 6 - Determine whether the distribution is a discrete...Ch. 6 - Stanley Cup The Stanley Cup is a best-of-seven...Ch. 6 - Expected Value of Three-Card Poker A popular...Ch. 6 - Determine whether the probability experiment...Ch. 6 - Emergency Room Visits The probability that a...Ch. 6 - Driving Age According to a Gallup poll, 60% of...Ch. 6 - Consider a binomial probability distribution with...Ch. 6 - State the condition required to use the Empirical...Ch. 6 - In sampling from finite populations without...Ch. 6 - Self-Injury According to the article...Ch. 6 - Prob. 1CTCh. 6 - Determine whether the distribution is a discrete...Ch. 6 - Prob. 3CTCh. 6 - Prob. 4CTCh. 6 - State the criteria that must be met for an...Ch. 6 - Determine whether the probability experiment...Ch. 6 - According to a study conducted by CESI Debt...Ch. 6 - Suppose the adult American population is equally...Ch. 6 - Consider a binomial probability distribution with...Ch. 6 - A woman who was shopping in Los Angeles had her...Ch. 6 - Using the information provided, describe, through...Ch. 6 - Does it appear that, on average, the Neulnders...Ch. 6 - Using the mean number of freights purchased per...Ch. 6 - Is it appropriate to estimate the average cost of...Ch. 6 - Throughout the picturesque valleys of...Ch. 6 - Throughout the picturesque valleys of...
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