Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 11.2, Problem 21E
In an experiment to investigate the effect of “cement factor”(number of sacks of cement per cubic yard) on flexural strength of the resulting concrete (“Studies of Flexural Strength of Concrete. Part 3: Effects of Variation in Testing Procedure,” Proceedings, ASTM,1957: 1127–1139), I = 3 different factor values were used, J = 5 different batches of cement were selected, and K = 2 beams were cast from each cement factor/batch combination. Sums of squares include SSA = 22,941.80, SSB = 22,765.53, SSE = 15,253.50,and SST = 64,954.70. Construct the ANOVA table. Then, assuming a mixed model with cement factor (A) fixed and batches (B) random, test the three pairs of hypotheses of interest at level .05.
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We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…
Negate the following compound statement using De Morgans's laws.
Chapter 11 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 11.1 - An experiment was carried out to investigate the...Ch. 11.1 - Four different coatings are being considered for...Ch. 11.1 - Prob. 3ECh. 11.1 - In an experiment to see whether the amount of...Ch. 11.1 - In an experiment to assess the effect of the angle...Ch. 11.1 - A particular county employs three assessors who...Ch. 11.1 - Prob. 7ECh. 11.1 - The paper Exercise Thermoregulation and...Ch. 11.1 - The article The Effects of a Pneumatic Stool and a...Ch. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - The power curves of Figures 10.5 and 10.6 can be...Ch. 11.2 - In an experiment to assess the effects of curing...Ch. 11.2 - Prob. 17ECh. 11.2 - The accompanying data resulted from an experiment...Ch. 11.2 - A two-way ANOVA was carried out to assess the...Ch. 11.2 - The article Fatigue Limits of Enamel Bonds with...Ch. 11.2 - In an experiment to investigate the effect of...Ch. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.3 - The output of a continuous extruding machine that...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Nickel titanium (NiTi) shape memory alloy (SMA)...Ch. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - The article The Responsiveness of Food Sales to...Ch. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.4 - The accompanying data resulted from an experiment...Ch. 11.4 - The accompanying data resulted from a 23...Ch. 11.4 - In a study of processes used to remove impurities...Ch. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - a. In a 24 experiment, suppose two blocks are to...Ch. 11.4 - a. An experiment was carried out to investigate...Ch. 11.4 - Prob. 46ECh. 11.4 - a. In a seven-factor experiment (A,, G), suppose a...Ch. 11.4 - The article Applying Design of Experiments to...Ch. 11 - The results of a study on the effectiveness of...Ch. 11 - Prob. 51SECh. 11 - Prob. 52SECh. 11 - In an automated chemical coating process, the...Ch. 11 - Coal-fired power plants used in the electrical...Ch. 11 - Impurities in the form of iron oxides lower the...Ch. 11 - Factorial designs have been used in forestry to...Ch. 11 - Prob. 57SECh. 11 - Prob. 58SECh. 11 - The bond strength when mounting an integrated...Ch. 11 - Prob. 60SECh. 11 - Prob. 61SE
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- Negate the following compound statement using De Morgans's laws.arrow_forwardQuestion 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- Characterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forwardLet G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forwardProve sufficiency of the condition for a graph to be bipartite that is, prove that if G hasno odd cycles then G is bipartite as follows:Assume that the statement is false and that G is an edge minimal counterexample. That is, Gsatisfies the conditions and is not bipartite but G − e is bipartite for any edge e. (Note thatthis is essentially induction, just using different terminology.) What does minimality say aboutconnectivity of G? Can G − e be disconnected? Explain why if there is an edge between twovertices in the same part of a bipartition of G − e then there is an odd cyclearrow_forward
- Let G be a connected graph that does not have P4 or C4 as an induced subgraph (i.e.,G is P4, C4 free). Prove that G has a vertex adjacent to all othersarrow_forwardWe consider a one-period market with the following properties: the current stock priceis S0 = 4. At time T = 1 year, the stock has either moved up to S1 = 8 (with probability0.7) or down towards S1 = 2 (with probability 0.3). We consider a call option on thisstock with maturity T = 1 and strike price K = 5. The interest rate on the money marketis 25% yearly.(a) Find the replicating portfolio (φ, ψ) corresponding to this call option.(b) Find the risk-neutral (no-arbitrage) price of this call option.(c) We now consider a put option with maturity T = 1 and strike price K = 3 onthe same market. Find the risk-neutral price of this put option. Reminder: A putoption gives you the right to sell the stock for the strike price K.1(d) An investor with initial capital X0 = 0 wants to invest on this market. He buysα shares of the stock (or sells them if α is negative) and buys β call options (orsells them is β is negative). He invests the cash balance on the money market (orborrows if the amount is…arrow_forwardDetermine if the two statements are equivalent using a truth tablearrow_forward
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