Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Chapter 6.3, Problem 32E
The Boston Fire Department receives 911 calls at a
- a. What is the mean time between 911 calls to the Boston Fire Department in minutes?
- b. Using the mean in part (a), show the probability density
function for the time between 911 calls in minutes. - c. What is the probability that there will be less than one hour between 911 calls?
- d. What is the probability that there will be 30 minutes or more between 911 calls?
- e. What is the probability that there will be more than 5 minutes, but less than 20 minutes between 911 calls?
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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
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(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 6 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Ch. 6.1 - The random variable x is known to be uniformly...Ch. 6.1 - The random variable x is known to be uniformly...Ch. 6.1 - Cincinnati to Tampa Flight Time. Delta Airlines...Ch. 6.1 - Prob. 4ECh. 6.1 - 5. In October 2012, Apple introduced a much...Ch. 6.1 - 6. A Gallup Daily Tracking Survey found that the...Ch. 6.1 - 7. Suppose we are interested in bidding on a piece...Ch. 6.2 - Using Figure 6.4 as a guide, sketch a normal curve...Ch. 6.2 - A random variable is normally distributed with a...Ch. 6.2 - 10. Draw a graph for the standard normal...
Ch. 6.2 - 11. Given that z is a standard normal random...Ch. 6.2 - 12. Given that z is a standard normal random...Ch. 6.2 - 13. Given that z is a standard normal random...Ch. 6.2 - Prob. 14ECh. 6.2 - Given that z is a standard normal random variable,...Ch. 6.2 - Given that z is a standard normal random variable,...Ch. 6.2 - The mean cost of domestic airfares in the United...Ch. 6.2 - The average return for large-cap domestic stock...Ch. 6.2 - Automobile Repair Costs. Automobile repair costs...Ch. 6.2 - Gasoline Prices. Suppose that the average price...Ch. 6.2 - Mensa Membership. A person must score in the upper...Ch. 6.2 - Television Viewing. Suppose that the mean daily...Ch. 6.2 - Time to Complete Final Exam. The time needed to...Ch. 6.2 - Labor Day Travel Costs. The American Automobile...Ch. 6.2 - New York City is the most expensive city in the...Ch. 6.3 - 32. Consider the following exponential probability...Ch. 6.3 - Prob. 27ECh. 6.3 - 34. Battery life between charges for the Motorola...Ch. 6.3 - 35. The time between arrivals of vehicles at a...Ch. 6.3 - 36. Comcast Corporation is the largest cable...Ch. 6.3 - 37. Wendy’s restaurant has been recognized for...Ch. 6.3 - 38. The Boston Fire Department receives 911 calls...Ch. 6 - 39. A business executive, transferred from Chicago...Ch. 6 - NCAA Scholarships. The NCAA estimates that the...Ch. 6 - Production Defects. Motorola used the normal...Ch. 6 - During early 2012, economic hardship was...Ch. 6 - The port of South Louisiana, located along 54...Ch. 6 - Service Contract Offer. Ward Doering Auto Sales is...Ch. 6 - Wedding Costs. The XO Group Inc. conducted a 2015...Ch. 6 - College Admissions Test Scores. Assume that the...Ch. 6 - College Graduates Starting Salaries. According to...Ch. 6 - 48. A machine fills containers with a particular...Ch. 6 - Prob. 43SECh. 6 - Prob. 44SECh. 6 - 53. Do you dislike waiting in line? Supermarket...Ch. 6 - 54. The time (in minutes) between telephone calls...
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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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