Applied Statistics and Probability for Engineers
Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 11, Problem 108SE
To determine

  • Find a regression line.
  • Explain whether the regression significant at α=0.05.
  • Conclude about the role of regression analysis to establish a cause and effect relationship.

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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 11 Solutions

Applied Statistics and Probability for Engineers

Ch. 11.2 - Prob. 11ECh. 11.2 - 11-12. An article in the Journal of Environmental...Ch. 11.2 - 11-13. A rocket motor is manufactured by bonding...Ch. 11.2 - 11-14. Go Tutorial An article in the Journal of...Ch. 11.2 - 11-15 An article in the Journal of the...Ch. 11.2 - 11-16. An article in Wood Science and Technology...Ch. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - 11-20. Show that in a simple linear regression...Ch. 11.2 - 11-21. Consider the simple linear regression model...Ch. 11.2 - 11-22. Suppose that we wish to fit a regression...Ch. 11.4 - 11-23. Recall the regression of percent body fat...Ch. 11.4 - Prob. 24ECh. 11.4 - 11-25. Suppose that in Exercise 11-24 weight is...Ch. 11.4 - 11-26. Consider the simple linear regression model...Ch. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - 11-31. Consider the National Football League data...Ch. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - 11-35. Consider the data from Exercise 11-9 on y =...Ch. 11.4 - Prob. 36ECh. 11.4 - 11-37. Consider the data from Exercise 11-13, on y...Ch. 11.4 - 11-38. Consider the data from Exercise 11-12 on y...Ch. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 44ECh. 11.6 - 11-45. Using the regression from Exercise...Ch. 11.6 - 11-46. Q Using the regression from Exercise...Ch. 11.6 - 11-47. Refer to the data in Exercise 11-3 on y =...Ch. 11.6 - 1-48. Exercise 11-4 presented data on roadway...Ch. 11.6 - 11-49. Refer to the NFL quarterback ratings data...Ch. 11.6 - Prob. 50ECh. 11.6 - 11-51. Exercise 11-7 presented data on y = steam...Ch. 11.6 - 11-52. Exercise 11-8 presented gasoline mileage...Ch. 11.6 - Prob. 53ECh. 11.6 - Prob. 54ECh. 11.6 - Prob. 55ECh. 11.6 - 11-56. Exercise 11-12 presented data on chloride...Ch. 11.6 - 11-57. Refer to the data in Exercise 11-13 on...Ch. 11.6 - Prob. 58ECh. 11.6 - Prob. 59ECh. 11.7 - 11-60. Consider the simple linear regression model...Ch. 11.7 - 11-61. Repeat Exercise 11-60 using an error term...Ch. 11.7 - 11-62. Refer to the compressive strength data in...Ch. 11.7 - 11-63. Refer to the NFL quarterback ratings data...Ch. 11.7 - 11-64. Refer to the data in Exercise 11-6 on...Ch. 11.7 - 11-65. Refer to the data in Exercise 11-7 on y =...Ch. 11.7 - 11-66. Refer to the gasoline mileage data in...Ch. 11.7 - Prob. 67ECh. 11.7 - Prob. 68ECh. 11.7 - 11-69. Refer to Exercise 11-12. which presented...Ch. 11.7 - Prob. 70ECh. 11.7 - 11-71. Consider the rocket propellant data in...Ch. 11.7 - 11-72. Consider the data in Exercise 11-9 on y =...Ch. 11.7 - Prob. 73ECh. 11.7 - Prob. 74ECh. 11.7 - Prob. 75ECh. 11.8 - 11-76. Suppose that data are obtained from 20...Ch. 11.8 - 11-77. Suppose that data are obtained from 20...Ch. 11.8 - Prob. 78ECh. 11.8 - 11-79. A random sample of 50 observations was made...Ch. 11.8 - 11-80. The data in Table E11-6 gave x = the water...Ch. 11.8 - Prob. 81ECh. 11.8 - 11-82. The weight and systolic blood pressure of...Ch. 11.8 - Prob. 83ECh. 11.8 - Prob. 84ECh. 11.8 - 11-85. Refer to the NFL quarterback ratings data...Ch. 11.8 - Prob. 86ECh. 11.9 - Prob. 87ECh. 11.9 - Prob. 88ECh. 11.9 - 11-89. An electric utility is interested in...Ch. 11.10 - Prob. 90ECh. 11.10 - 11-91. The compressive strength of an alloy...Ch. 11.10 - Prob. 92ECh. 11.10 - Prob. 93ECh. 11.10 - Prob. 94ECh. 11.10 - 11-95 Consider the propellant data is Exercise...Ch. 11 - Prob. 96SECh. 11 - Prob. 97SECh. 11 - 11-98. The strength of paper used in the...Ch. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 101SECh. 11 - Prob. 102SECh. 11 - 11-103. An article in the Journal of Applied...Ch. 11 - 11-104. Two different methods can be used for...Ch. 11 - 11-105. The grams of solids removed from a...Ch. 11 - Prob. 106SECh. 11 - 11-107. The data in Table E11-20 related diamond...Ch. 11 - Prob. 108SECh. 11 - Prob. 109SECh. 11 - Prob. 110SECh. 11 - 11-111. Consider the simple linear regression...Ch. 11 - Prob. 112SECh. 11 - Prob. 113SECh. 11 - Prob. 114SECh. 11 - Prob. 115SECh. 11 - Prob. 116SE
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