Basic Business Statistics, Student Value Edition (13th Edition)
13th Edition
ISBN: 9780321946393
Author: Mark L. Berenson, David M. Levine, Kathryn A. Szabat
Publisher: PEARSON
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Chapter 12, Problem 12PS
Use the following
a. Compute the expected frequency for each cell.
b. Compute
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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 12 Solutions
Basic Business Statistics, Student Value Edition (13th Edition)
Ch. 12 - Determine the critical value of 2 with 1 degree of...Ch. 12 - Determine the critical value of 2 with 1 degree of...Ch. 12 - Use the following contingency table: a. Compute...Ch. 12 - Use the following contingency table: a. Compare...Ch. 12 - Prob. 5PSCh. 12 - Prob. 6PSCh. 12 - Do males or females feel more tense or stressed...Ch. 12 - Prob. 8PSCh. 12 - Prob. 9PSCh. 12 - Prob. 10PS
Ch. 12 - Consider a contingency table, with two rows and...Ch. 12 - Use the following contingency table: a. Compute...Ch. 12 - Use the following contingency table: a. Compute...Ch. 12 - Prob. 14PSCh. 12 - Prob. 15PSCh. 12 - Social media users use a variety of devices to...Ch. 12 - Repeat (a) and (b) of Problem 12.16, assuming that...Ch. 12 - Prob. 18PSCh. 12 - Prob. 19PSCh. 12 - Prob. 20PSCh. 12 - Prob. 21PSCh. 12 - Prob. 22PSCh. 12 - Prob. 23PSCh. 12 - Prob. 24PSCh. 12 - Prob. 25PSCh. 12 - Prob. 26PSCh. 12 - Using Table E.6, determine the lower-and...Ch. 12 - Using Table E.6, determine the lower-tail critical...Ch. 12 - Prob. 29PSCh. 12 - Prob. 30PSCh. 12 - Prob. 31PSCh. 12 - The following information is available for two...Ch. 12 - From Problem 12.32 , at the 0.05 level of...Ch. 12 - In Problems 12.32 and 12.33, what is your...Ch. 12 - A vice president for marketing recruits 20 college...Ch. 12 - Prob. 36PSCh. 12 - Prob. 37PSCh. 12 - The management of a hotel has the business...Ch. 12 - The lengths of life (in hours) of a sample of 40...Ch. 12 - Brand valuations are critical to CEOs, financial...Ch. 12 - A bank with a branch located in a commercial...Ch. 12 - Prob. 42PSCh. 12 - Prob. 43PSCh. 12 - Prob. 44PSCh. 12 - A pet food company has the business objective of...Ch. 12 - A hospital conducted a study of the waiting time...Ch. 12 - Prob. 47PSCh. 12 - An advertising agency has been hired by a...Ch. 12 - Prob. 49PSCh. 12 - The more costly and time consuming it is to export...Ch. 12 - Prob. 51PSCh. 12 - Prob. 52PSCh. 12 - Prob. 53PSCh. 12 - Prob. 54PSCh. 12 - Prob. 55PSCh. 12 - Prob. 56PSCh. 12 - Prob. 57PSCh. 12 - Prob. 58PSCh. 12 - Prob. 59PS
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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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