Loose-leaf For Applied Statistics In Business And Economics
5th Edition
ISBN: 9781259328527
Author: David Doane, Lori Seward Senior Instructor of Operations Management
Publisher: McGraw-Hill Education
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Chapter 1.5, Problem 16SE
When Pennsylvania repealed a law that required motorcycle riders to wear helmets, a news headline reported, “Deaths Soar After Repeal of Helmet Law.” After reading the story. Bill said. “But it’s just a
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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 1 Solutions
Loose-leaf For Applied Statistics In Business And Economics
Ch. 1.3 - Give an example of how statistics might be useful...Ch. 1.3 - Give an example of how statistics might be useful...Ch. 1.3 - (a) Should the average business school graduate...Ch. 1.3 - Many college graduates will not use very much...Ch. 1.5 - Recently, the same five winning numbers (4, 21,...Ch. 1.5 - A National Health Interview Survey conducted by...Ch. 1.5 - A study found that radar detector users have lower...Ch. 1.5 - A lottery winner told how he picked his six-digit...Ch. 1.5 - Smokers are much more likely to speed, run red...Ch. 1.5 - An ad for a cell phone service claims that its...
Ch. 1.5 - What logical or ethical problems do you see in...Ch. 1.5 - A recent study of 231,164 New Jersey heart attack...Ch. 1.5 - When Pennsylvania repealed a law that required...Ch. 1 - Define (a) statistic; (b) statistics.Ch. 1 - List three reasons to study statistics.Ch. 1 - List three applications of statistics.Ch. 1 - List four skills needed by statisticians. Why are...Ch. 1 - List three practical challenges faced by...Ch. 1 - List three ethical challenges faced by...Ch. 1 - List five pitfalls or logical errors that may...Ch. 1 - A survey of beginning students showed that a...Ch. 1 - Under a recent U.S. Food and Drug Administration...Ch. 1 - A statistical consultant was retained by a linen...Ch. 1 - Ergonomics is the science of making sure that...Ch. 1 - Analysis of 1,064 deaths of famous popular...Ch. 1 - Prob. 22CECh. 1 - Prob. 23CECh. 1 - A European study of thousands of men found that...Ch. 1 - A research study showed that 7 percent of A...Ch. 1 - A research study showed that adolescents who...Ch. 1 - Prob. 27CECh. 1 - (a) Which of these two displays (table or graph)...Ch. 1 - (a) Which of these two displays (table or graph)...
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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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