EBK BASIC BUSINESS STATISTICS
14th Edition
ISBN: 9780134685090
Author: STEPHAN
Publisher: VST
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Chapter 4, Problem 38PS
If there are 10 multiple-choice question on an exam, each having three possible answer, how many different sequences of answers are there?
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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 4 Solutions
EBK BASIC BUSINESS STATISTICS
Ch. 4 - Three coins are tossed. a. Give an example of a...Ch. 4 - An urn contain 12 red balls and 8 white balls. One...Ch. 4 - Consider the following contingency table: What is...Ch. 4 - Consider the following contingency table: What is...Ch. 4 - For each of the following, indicate whether the...Ch. 4 - For each of the following, state whether the...Ch. 4 - Which of the following events occur with a...Ch. 4 - Do Millennials or Gen-Xers feel more tense or...Ch. 4 - Referring to the contingency table in Problem 4.8,...Ch. 4 - How will markers change their social media use in...
Ch. 4 - Referring to the contingency table in Problem...Ch. 4 - Have the gains in student learning attributed to...Ch. 4 - Do Generation X and Boomers differ in how they use...Ch. 4 - A survey of 1,520 Americans, adults asked, “Do...Ch. 4 - Each year ratings are compiled concerning the...Ch. 4 - Consider the following contingency table: What is...Ch. 4 - Consider the following contingency table: What is...Ch. 4 - If P(AandB)=0.4andP(B)=0.8,findP(AB).Ch. 4 - Prob. 19PSCh. 4 - ...Ch. 4 - Do Millennials or Gen-Xers feel more tense...Ch. 4 - How will marketers change their social media use...Ch. 4 - Do generation X and Boomers differ in how they use...Ch. 4 - Have the grains in student learning attributed to...Ch. 4 - A survey of 1,520 Americans adults asked “Do you...Ch. 4 - Each year, rating are compiled concerning the...Ch. 4 - In 42 of the 66 years from 1950 through 2010 (in...Ch. 4 - A standard deck of cards is being used to play a...Ch. 4 - A box of nine iPhone 7 cellphones contains two red...Ch. 4 - ...Ch. 4 - ...Ch. 4 - In Example 4.10 to suppose that the probability...Ch. 4 - Big Commerce launched a study to analyze modern...Ch. 4 - Olive Construction Company is determining whether...Ch. 4 - The 2016 Global Information Security Workforce...Ch. 4 - The editor of a textbook published company is...Ch. 4 - A municipal bond service has three rating...Ch. 4 - If there are 10 multiple-choice question on an...Ch. 4 - A lock on a bank vault consists of three dials,...Ch. 4 - a. If a coin is tossed seven times, how many...Ch. 4 - A particular brand of women’s jeans is available...Ch. 4 - Prob. 42PSCh. 4 - A team is being formed that includes four...Ch. 4 - In the National Basketball League there are five...Ch. 4 - Referring to Problem 4.44 how many different...Ch. 4 - A gardener has six rows available in his vegetable...Ch. 4 - How many different ways can a senior project...Ch. 4 - Four member of a group of 10 people are to be...Ch. 4 - A student has seven books that she would like to...Ch. 4 - A daily lottery is conducted in which 2 winning...Ch. 4 - There are 15 exercise bikes in a fitness store...Ch. 4 - What are the differences between a priori...Ch. 4 - What is the difference between a simple event and...Ch. 4 - How can you use the general addition rule to find...Ch. 4 - What is the difference between mutually exclusive...Ch. 4 - How does conditional probability relate to the...Ch. 4 - How does the multiplication rule differ for events...Ch. 4 - How can you use Bayes theorem in light of new...Ch. 4 - In Bayes’ theorem, how does the prior...Ch. 4 - What is the difference between Counting Rule 1 and...Ch. 4 - What is the difference between a permutation and...Ch. 4 - A survey by Accenture indicated that 64% of...Ch. 4 - Chartered Institute of personnel and Development...Ch. 4 - To better understand the website builder market,...Ch. 4 - Content Marketing institute provides insight on...Ch. 4 - The CMO survey collects and dissemination the...
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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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