EBK STATISTICS FOR BUSINESS & ECONOMICS
12th Edition
ISBN: 8220100460463
Author: Anderson
Publisher: CENGAGE L
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Chapter 5.5, Problem 35E
In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005).
- a. In a sample of 10 workers, what is the
probability that exactly 3 workers take public transportation daily? - b. In a sample of 10 workers, what is the probability that at least 3 workers take public transportation daily?
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T1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an
independent set and m(G) = |E(G)|.
(i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The
neighborhood of a vertex in a triangle free graph must be independent; all edges have at least
one end in a vertex cover.
(ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you
may need to use either elementary calculus or the arithmetic-geometric mean inequality.
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 5 Solutions
EBK STATISTICS FOR BUSINESS & ECONOMICS
Ch. 5.1 - Consider the experiment of tossing a coin twice....Ch. 5.1 - Consider the experiment of a worker assembling a...Ch. 5.1 - Three students scheduled interviews for summer...Ch. 5.1 - In January the U.S. unemployment rate dropped to...Ch. 5.1 - To perform a certain type of blood analysis, lab...Ch. 5.1 - Listed is a series of experiments and associated...Ch. 5.2 - The probability distribution for the random...Ch. 5.2 - The following data were collected by counting the...Ch. 5.2 - For unemployed persons in the United States, the...Ch. 5.2 - The percent frequency distributions of job...
Ch. 5.2 - A technician services mailing machines at...Ch. 5.2 - The two largest cable providers are Comcast Cable...Ch. 5.2 - A psychologist determined that the number of...Ch. 5.2 - The following table is a partial probability...Ch. 5.3 - The following table provides a probability...Ch. 5.3 - The following table provides a probability...Ch. 5.3 - The number of students taking the SAT has risen to...Ch. 5.3 - The American Housing Survey reported the following...Ch. 5.3 - The National Basketball Association (NBA) records...Ch. 5.3 - The probability distribution for damage claims...Ch. 5.3 - The following probability distributions of job...Ch. 5.3 - The demand for a product of Carolina Industries...Ch. 5.3 - Prob. 23ECh. 5.3 - The J. R. Ryland Computer Company is considering a...Ch. 5.4 - Given below is a bivariate distribution for the...Ch. 5.4 - A person is interested in constructing a...Ch. 5.4 - The Chamber of Commerce in a Canadian city has...Ch. 5.4 - PortaCom has developed a design for a high-quality...Ch. 5.4 - J.P. Morgan Asset Management publishes information...Ch. 5.4 - In addition to the information in exercise 29 on...Ch. 5.5 - Consider a binomial experiment with two trials and...Ch. 5.5 - Consider a binomial experiment with n = 10 and p =...Ch. 5.5 - Consider a binomial experiment with n = 20 and p =...Ch. 5.5 - A Harris Interactive survey for InterContinental...Ch. 5.5 - In San Francisco, 30% of workers take public...Ch. 5.5 - When a new machine is functioning properly, only...Ch. 5.5 - A Randstad/Harris interactive survey reported that...Ch. 5.5 - Military radar and missile detection systems are...Ch. 5.5 - Twelve of the top 20 finishers in the 2009 PGA...Ch. 5.5 - The Census Bureaus Current Population Survey shows...Ch. 5.5 - A university found that 20% of its students...Ch. 5.5 - According to a survey conducted by TD Ameritrade,...Ch. 5.5 - Twenty-three percent of automobiles are not...Ch. 5.6 - Consider a Poisson distribution with = 3. a....Ch. 5.6 - Consider a Poisson distribution with a mean of two...Ch. 5.6 - Phone calls arrive at the rate of 48 per hour at...Ch. 5.6 - During the period of time that a local university...Ch. 5.6 - More than 50 million guests stay at bed and...Ch. 5.6 - Airline passengers arrive randomly and...Ch. 5.6 - An average of 15 aircraft accidents occur each...Ch. 5.6 - The National Safety Council (NSC) estimates that...Ch. 5.7 - Suppose N = 10 and r = 3. Compute the...Ch. 5.7 - Suppose N = 15 and r = 4. What is the probability...Ch. 5.7 - In a survey conducted by the Gallup Organization,...Ch. 5.7 - Blackjack, or twenty-one as it is frequently...Ch. 5.7 - Axline Computers manufactures personal computers...Ch. 5.7 - The Zagat Restaurant Survey provides food, decor,...Ch. 5.7 - The Troubled Asset Relief Program (TARP), passed...Ch. 5 - The Barrons Big Money Poll asked 131 investment...Ch. 5 - The American Association of Individual Investors...Ch. 5 - The budgeting process for a midwestern college...Ch. 5 - A bookstore at the Hartsfield-Jackson Airport in...Ch. 5 - The Knowles/Armitage (KA) group at Merrill Lynch...Ch. 5 - A survey showed that the average commuter spends...Ch. 5 - A political action group is planning to interview...Ch. 5 - Many companies use a quality control technique...Ch. 5 - The unemployment rate in the state of Arizona is...Ch. 5 - A poll conducted by Zogby International showed...Ch. 5 - Cars arrive at a car wash randomly and...Ch. 5 - A new automated production process averages 1.5...Ch. 5 - A regional director responsible for business...Ch. 5 - Customer arrivals at a bank are random and...Ch. 5 - A deck of playing cards contains 52 cards, four of...Ch. 5 - U.S. News World Reports ranking of Americas best...
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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
- Question 4: Determine if pair of statements A and B are equivalent or not, using truth table. A. (~qp)^~q в. р л~9arrow_forwardDetermine 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_forward
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