Understandable Statistics: Concepts and Methods
Understandable Statistics: Concepts and Methods
12th Edition
ISBN: 9781337119917
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 4.3, Problem 3P

a.

To determine

Explain why the combinations rule or permutations rule should be used for the given situation.

b.

To determine

Give reason for that the combinations rule or permutations rule should be used for the given scenario.

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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 4 Solutions

Understandable Statistics: Concepts and Methods

Ch. 4.1 - Critical Thinking Consider a family with 3...Ch. 4.1 - Prob. 12PCh. 4.1 - Prob. 13PCh. 4.1 - Critical Thinking (a) Explain why 0.41 cannot be...Ch. 4.1 - Myers-Briggs: Personality Types Isabel Briggs...Ch. 4.1 - General: Roll a Die (a) If you roll a single die...Ch. 4.1 - Psychology: Creativity When do creative people get...Ch. 4.1 - Agriculture: Cotton A botanist has developed a new...Ch. 4.1 - Expand Your Knowledge: Odds in Favor Sometimes...Ch. 4.1 - Expand Your Knowledge: Odds Against Betting odds...Ch. 4.1 - Business: Customers John runs a computer software...Ch. 4.2 - Statistical Literacy If two events are mutually...Ch. 4.2 - Statistical Literacy If two events A and B are...Ch. 4.2 - Basic Computation: Addition Rule Given P(A) = 0.3...Ch. 4.2 - Basic Computation: Addition Rule Given P(A) = 0.7...Ch. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.2 - Prob. 7PCh. 4.2 - Prob. 8PCh. 4.2 - Prob. 9PCh. 4.2 - Prob. 10PCh. 4.2 - Prob. 11PCh. 4.2 - Prob. 12PCh. 4.2 - Prob. 13PCh. 4.2 - Prob. 14PCh. 4.2 - Prob. 15PCh. 4.2 - Environmental: Land Formations Arches National...Ch. 4.2 - Prob. 17PCh. 4.2 - General: Roll Two Dice You roll two fair dice, a...Ch. 4.2 - Prob. 19PCh. 4.2 - Prob. 20PCh. 4.2 - Prob. 21PCh. 4.2 - General: Deck of Cards You draw two cards from a...Ch. 4.2 - General: Deck of Cards You draw two cards from a...Ch. 4.2 - Prob. 24PCh. 4.2 - Marketing: Toys USA Today gave the information...Ch. 4.2 - Prob. 26PCh. 4.2 - Prob. 27PCh. 4.2 - Prob. 28PCh. 4.2 - Prob. 29PCh. 4.2 - Survey: Medical Tests Diagnostic tests of medical...Ch. 4.2 - Survey: Lung/Heart In an article titled Diagnostic...Ch. 4.2 - Survey: Customer Loyalty Are customers more loyal...Ch. 4.2 - Franchise Stores: Profits Wing Foot is a shoe...Ch. 4.2 - Education: College of Nursing At Litchfield...Ch. 4.2 - Medical: Tuberculosis The state medical school has...Ch. 4.2 - Prob. 36PCh. 4.2 - Brain Teasers Assume A and B are events such that...Ch. 4.2 - Brain Teasers Assume A and B are events such that...Ch. 4.2 - Prob. 39PCh. 4.2 - Prob. 40PCh. 4.2 - Prob. 41PCh. 4.2 - Prob. 42PCh. 4.2 - Prob. 43PCh. 4.2 - Prob. 44PCh. 4.2 - Prob. 45PCh. 4.2 - Prob. 46PCh. 4.2 - Prob. 47PCh. 4.2 - Prob. 48PCh. 4.2 - Prob. 49PCh. 4.2 - Prob. 50PCh. 4.2 - Prob. 51PCh. 4.2 - Prob. 52PCh. 4.3 - Prob. 1PCh. 4.3 - Prob. 2PCh. 4.3 - Prob. 3PCh. 4.3 - Prob. 4PCh. 4.3 - Tree Diagram (a) Draw a tree diagram to display...Ch. 4.3 - Tree Diagram (a) Draw a tree diagram to display...Ch. 4.3 - Prob. 7PCh. 4.3 - Prob. 8PCh. 4.3 - Prob. 9PCh. 4.3 - Multiplication Rule for Counting A sales...Ch. 4.3 - Counting: Agriculture Barbara is a research...Ch. 4.3 - Counting: Outcomes You toss a pair of dice. (a)...Ch. 4.3 - Compute P5,2.Ch. 4.3 - Prob. 14PCh. 4.3 - Compute P7,7.Ch. 4.3 - Compute P9,9.Ch. 4.3 - Compute C5,2.Ch. 4.3 - Compute C8,3.Ch. 4.3 - Prob. 19PCh. 4.3 - Prob. 20PCh. 4.3 - Counting: Hiring There are three nursing positions...Ch. 4.3 - Counting: Lottery In the Cash Now lottery game...Ch. 4.3 - Counting: Sports The University of Montana ski...Ch. 4.3 - Counting: Sales During the Computer Daze special...Ch. 4.3 - Counting: Hiring There are 15 qualified applicants...Ch. 4.3 - Counting: Grading One professor grades homework by...Ch. 4.3 - Prob. 27PCh. 4.3 - Counting: Powerball The Viewpoint of this section,...Ch. 4 - Prob. 1CRPCh. 4 - Prob. 2CRPCh. 4 - Prob. 3CRPCh. 4 - Prob. 4CRPCh. 4 - Prob. 5CRPCh. 4 - Prob. 6CRPCh. 4 - Prob. 7CRPCh. 4 - Critical Thinking For a class activity, your group...Ch. 4 - Prob. 9CRPCh. 4 - Prob. 10CRPCh. 4 - Prob. 11CRPCh. 4 - Prob. 12CRPCh. 4 - Prob. 13CRPCh. 4 - Prob. 14CRPCh. 4 - Prob. 15CRPCh. 4 - Prob. 16CRPCh. 4 - Prob. 17CRPCh. 4 - Prob. 18CRPCh. 4 - Prob. 19CRPCh. 4 - Prob. 20CRPCh. 4 - Look at Figure 4-11, Whos Cracking the Books? (a)...Ch. 4 - Prob. 2LCCh. 4 - Prob. 1UT
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