Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 3, Problem 114SE
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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.
Negate the following compound statement using De Morgans's laws.
Chapter 3 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 3.1 - A concrete beam may fail either by shear (S) or...Ch. 3.1 - Using the experiment in Example 3.3, define two...Ch. 3.1 - Let X = the number of nonzero digits in a randomly...Ch. 3.1 - If the sample space S is an infinite set, does...Ch. 3.1 - Starting at a fixed time, each car entering an...Ch. 3.1 - For each random variable defined here, describe...Ch. 3.1 - Each time a component is tested, the trial is a...Ch. 3.1 - An individual named Claudius is located at the...Ch. 3.1 - The number of pumps in use at both a six-pump...Ch. 3.2 - Let X be the number of students who show up for a...
Ch. 3.2 - Airlines sometimes overbook flights. Suppose that...Ch. 3.2 - A mail-order computer business has six telephone...Ch. 3.2 - A contractor is required by a county planning...Ch. 3.2 - Many manufacturers have quality control programs...Ch. 3.2 - Some parts of California are particularly...Ch. 3.2 - A now batterys voltage may be acceptable (A) or...Ch. 3.2 - Two fair six-sided dice are tossed independently....Ch. 3.2 - A library subscribes to two different weekly news...Ch. 3.2 - Three couples and two single individuals have been...Ch. 3.2 - Suppose that you read through this years issues of...Ch. 3.2 - Refer to Exercise 13, and calculate and graph the...Ch. 3.2 - A branch of a certain bank in New York City has...Ch. 3.2 - An insurance company offers its policyholders a...Ch. 3.2 - In Example 3.12, let Y = the number of girls born...Ch. 3.2 - Alvie Singer lives at 0 in the accompanying...Ch. 3.2 - After all students have left the classroom, a...Ch. 3.2 - Show that the cdf F(x) is a nondecreasing...Ch. 3.3 - The pmf of the amount of memory X(GB) in a...Ch. 3.3 - An individual who has automobile insurance from a...Ch. 3.3 - Refer to Exercise 12 and calculate V(Y) and Y....Ch. 3.3 - A certain brand of upright freezer is available in...Ch. 3.3 - Let X be a Bernoulli rv with pmf as in Example...Ch. 3.3 - Suppose that the number of plants of a particular...Ch. 3.3 - A small market orders copies of a certain magazine...Ch. 3.3 - Let X be the damage incurred (in ) in a certain...Ch. 3.3 - The n candidates for a job have been ranked 1, 2,...Ch. 3.3 - Possible values of X, the number of components in...Ch. 3.3 - A chemical supply company currently has in stock...Ch. 3.3 - a. Draw a line graph of the pmf of X in Exercise...Ch. 3.3 - Use the definition in Expression (3.13) to prove...Ch. 3.3 - Suppose E(X) = 5 and E[X(X - 1)] = 27.5. What is...Ch. 3.3 - Write a general rule for E(X c) where c is a...Ch. 3.3 - A result called Chebyshevs inequality states that...Ch. 3.3 - If a X b, show that a E(X) b.Ch. 3.4 - Compute the following binomial probabilities...Ch. 3.4 - The article Should You Report That Fender-Bender?...Ch. 3.4 - NBC News reported on May 2. 2013. that 1 in 20...Ch. 3.4 - A company that produces fine crystal knows from...Ch. 3.4 - A particular telephone number is used to receive...Ch. 3.4 - Refer to the previous exercise. a. What is the...Ch. 3.4 - Suppose that 30% of all students who have to buy a...Ch. 3.4 - Exercise 30 (Section 3.3) gave the pmf of Y, the...Ch. 3.4 - A particular type of tennis racket comes in a...Ch. 3.4 - Twenty percent of all telephones of a certain type...Ch. 3.4 - The College Board reports that 2% of the 2 million...Ch. 3.4 - A certain type of flashlight requires two type-D...Ch. 3.4 - A very large batch of components has arrived at a...Ch. 3.4 - An ordinance requiring that a smoke detector be...Ch. 3.4 - A toll bridge charges 1.00 for passenger cars and...Ch. 3.4 - A student who is trying to write a paper for a...Ch. 3.4 - a. For fixed n, are there values of p(0 p 1) for...Ch. 3.4 - a. Show that b(x; n, 1 p) = b(n x; n, p). b....Ch. 3.4 - Show that E(X) = np when X is a binomial random...Ch. 3.4 - Customers at a gas station pay with a credit card...Ch. 3.4 - An airport limousine can accommodate up to four...Ch. 3.4 - Refer to Chebyshevs inequality given in Exercise...Ch. 3.5 - Eighteen individuals are scheduled to take a...Ch. 3.5 - Each of 12 refrigerators of a certain type has...Ch. 3.5 - An instructor who taught two sections of...Ch. 3.5 - A geologist has collected 10 specimens of basaltic...Ch. 3.5 - A personnel director interviewing 11 senior...Ch. 3.5 - Twenty pairs of individuals playing in a bridge...Ch. 3.5 - A second-stage smog alert has been called in a...Ch. 3.5 - The probability that a randomly selected box of a...Ch. 3.5 - A family decides to have children until it has...Ch. 3.5 - Three brothers and their wives decide to have...Ch. 3.5 - According to the article Characterizing the...Ch. 3.6 - The article Expectation Analysis of the...Ch. 3.6 - Let X be the number of material anomalies...Ch. 3.6 - Suppose that the number of drivers who travel...Ch. 3.6 - Consider writing onto a computer disk and then...Ch. 3.6 - An article in the Los Angeles Times (Dec. 3. 1993)...Ch. 3.6 - The Centers for Disease Control and Prevention...Ch. 3.6 - Suppose small aircraft arrive at a certain airport...Ch. 3.6 - Organisms are present in ballast water discharged...Ch. 3.6 - The number of requests for assistance received by...Ch. 3.6 - In proof testing of circuit boards, the...Ch. 3.6 - The article Reliability-Based Service-Life...Ch. 3.6 - Let X have a Poisson distribution with parameter ....Ch. 3.6 - Suppose that trees are distributed in a forest...Ch. 3.6 - Automobiles arrive at a vehicle equipment...Ch. 3.6 - a. In a Poisson process, what has to happen in...Ch. 3 - Consider a deck consisting of seven cards, marked...Ch. 3 - After shuffling a deck of 52 cards, a dealer deals...Ch. 3 - The negative binomial rv X was defined as the...Ch. 3 - Of all customers purchasing automatic garage-door...Ch. 3 - In some applications the distribution of a...Ch. 3 - A k-out-of-n system is one that will function if...Ch. 3 - A manufacturer of integrated circuit chips wishes...Ch. 3 - Of the people passing through an airport metal...Ch. 3 - An educational consulting firm is trying to decide...Ch. 3 - Consider a disease whose presence can be...Ch. 3 - Let p1 denote the probability that any particular...Ch. 3 - The purchaser of a power-generating unit requires...Ch. 3 - A plan for an executive travelers club has been...Ch. 3 - Forty percent of seeds from maize (modern-day com)...Ch. 3 - A trial has just resulted in a hung jury because...Ch. 3 - A reservation service employs five information...Ch. 3 - Grasshoppers arc distributed at random in a large...Ch. 3 - A newsstand has ordered five copies of a certain...Ch. 3 - Individuals A and B begin to play a sequence of...Ch. 3 - A test for the presence of a certain disease has...Ch. 3 - Prob. 114SECh. 3 - There are two Certified Public Accountants in a...Ch. 3 - The mode of a discrete random variable X with pmf...Ch. 3 - A computer disk storage device has ten concentric...Ch. 3 - If X is a hypergeometric rv, show directly from...Ch. 3 - Prob. 119SECh. 3 - Prob. 120SECh. 3 - Prob. 121SECh. 3 - Prob. 122SE
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- Question 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_forwardCharacterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forward
- Let 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_forwardLet 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_forward
- We 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_forwardQuestion 4: Determine if pair of statements A and B are equivalent or not, using truth table. A. (~qp)^~q в. р л~9arrow_forward
- Determine if the two statements are equalivalent using a truth tablearrow_forwardQuestion 3: p and q represent the following simple statements. p: Calgary is the capital of Alberta. A) Determine the value of each simple statement p and q. B) Then, without truth table, determine the va q: Alberta is a province of Canada. for each following compound statement below. pvq р^~q ~рл~q ~q→ p ~P~q Pq b~ (d~ ← b~) d~ (b~ v d) 0 4arrow_forward2. Let X be a random variable. (a) Show that, if E X2 = 1 and E X4arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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