Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Chapter 18, Problem 15E
Cattle Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the
- a) 95% of the cows studied gained between 45 and 67 pounds.
- b) We’re 95% sure that a cow fed this supplement will gain between 45 and 67 pounds.
- c) We’re 95% sure that the average weight gain among the cows in this study was between 45 and 67 pounds.
- d) The average weight gain of cows fed this supplement will be between 45 and 67 pounds 95% of the time.
- e) If this supplement is tested on another sample of cows, there is a 95% chance that their average weight gain will be between 45 and 67 pounds.
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In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Chapter 18 Solutions
Intro Stats
Ch. 18.2 - Every 10 years, the United States takes a census....Ch. 18.2 - Prob. 2JCCh. 18.2 - Prob. 3JCCh. 18.2 - Every 10 years, the United States takes a census....Ch. 18.2 - Prob. 5JCCh. 18.2 - Prob. 6JCCh. 18 - Salmon A specialty food company sells whole King...Ch. 18 - LSAT The LSAT (a test taken for law school...Ch. 18 - Prob. 3ECh. 18 - t-models, part II Using the t tables, software, or...
Ch. 18 - t-models, part III Describe how the shape, center,...Ch. 18 - Prob. 6ECh. 18 - Prob. 7ECh. 18 - Home sales again In the previous exercise, you...Ch. 18 - Prob. 9ECh. 18 - Prob. 10ECh. 18 - Prob. 11ECh. 18 - Prob. 12ECh. 18 - Prob. 13ECh. 18 - Prob. 14ECh. 18 - Cattle Livestock are given a special feed...Ch. 18 - Prob. 16ECh. 18 - Meal plan After surveying students at Dartmouth...Ch. 18 - Prob. 18ECh. 18 - Prob. 19ECh. 18 - Prob. 20ECh. 18 - Prob. 21ECh. 18 - Credit card charges A credit card company takes a...Ch. 18 - 23. Normal temperature The researcher described in...Ch. 18 - Parking Hoping to lure more shoppers downtown, a...Ch. 18 - 25. Normal temperatures, part II Consider again...Ch. 18 - 26. Parking II Suppose that, for budget planning...Ch. 18 - Speed of light In 1882, Michelson measured the...Ch. 18 - Prob. 28ECh. 18 - Prob. 29ECh. 18 - Prob. 30ECh. 18 - Prob. 31ECh. 18 - Prob. 32ECh. 18 - Prob. 33ECh. 18 - Golf balls The United States Golf Association...Ch. 18 - Prob. 35ECh. 18 - Computer lab fees The technology committee has...Ch. 18 - Marriage In 1960, census results indicated that...Ch. 18 - Prob. 38ECh. 18 - Prob. 39ECh. 18 - Prob. 40ECh. 18 - Prob. 41ECh. 18 - Prob. 42ECh. 18 - Prob. 43ECh. 18 - 44. Yogurt Consumer Reports tested 11 brands of...Ch. 18 - 45. Maze Psychology experiments sometimes involve...Ch. 18 - Prob. 46ECh. 18 - 47. Driving distance 2011 How far do professional...Ch. 18 - Prob. 48E
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