Applied Statistics in Business and Economics
5th Edition
ISBN: 9780077837303
Author: David Doane, Lori Seward Senior Instructor of Operations Management
Publisher: McGraw-Hill Education
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Chapter 3.7, Problem 21SE
(a) Use Excel to make 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 3 Solutions
Applied Statistics in Business and Economics
Ch. 3.1 - (a) Make a stem-and-leaf plot for these 24...Ch. 3.1 - (a) Make a stem-and-leaf plot for the number of...Ch. 3.1 - Prob. 3SECh. 3.2 - (a) The table shows the number of days on the...Ch. 3.2 - (a) The table shows raw scores on a state civil...Ch. 3.2 - (a) Make a frequency distribution and histogram...Ch. 3.2 - (a) Make a frequency distribution and histogram...Ch. 3.2 - (a) Make a frequency distribution and histogram...Ch. 3.2 - For each frequency distribution, suggest nice...Ch. 3.2 - Below are sorted data showing average spending per...
Ch. 3.4 - (a) Use Excel to prepare a line chart to display...Ch. 3.4 - Prob. 12SECh. 3.4 - Prob. 13SECh. 3.4 - (a) Use Excel to prepare a line chart to display...Ch. 3.5 - Prob. 15SECh. 3.5 - Prob. 16SECh. 3.6 - (a) Use Excel to prepare a 2-D pie chart for these...Ch. 3.6 - Prob. 19SECh. 3.6 - Prob. 20SECh. 3.7 - (a) Use Excel to make a scatter plot of the data...Ch. 3.7 - Prob. 22SECh. 3.7 - Prob. 23SECh. 3.7 - (a) Use Excel to make a scatter plot of the data,...Ch. 3 - Name two attractive features and two limitations...Ch. 3 - (a) What is a frequency distribution? (b) What are...Ch. 3 - (a) What is a histogram? (b) What does it show?Ch. 3 - (a) What is a bimodal histogram? (b) Explain the...Ch. 3 - (a) What is a scatter plot? (b) What do scatter...Ch. 3 - For what kind of data would we use a bar chart?...Ch. 3 - For what kind of data would we use a line chart?...Ch. 3 - (a) List the three most common types of charts in...Ch. 3 - (a) For what kind of data would we use a pie...Ch. 3 - Which types of charts can be used for time series...Ch. 3 - (a) When might we need a log scale? (b) What do...Ch. 3 - When might we use a stacked column chart? An area...Ch. 3 - List five deceptive graphical techniques.Ch. 3 - What is a pivot table? Why is it useful?Ch. 3 - The durations (minutes) of 26 electric power...Ch. 3 - The U.S. Postal Service will ship a Priority Mail,...Ch. 3 - A study of 40 U.S. cardiac care centers showed the...Ch. 3 - Prob. 28CECh. 3 - Prob. 29CECh. 3 - Below are batting averages of the New York Yankees...Ch. 3 - Download the full data set of measurements of...Ch. 3 - Prob. 32CECh. 3 - Download the full data set from the McGraw-Hill...Ch. 3 - (a) What kind of display is this? (b) Identify its...Ch. 3 - (a) What kind of display is this? (b) Identify its...Ch. 3 - Prob. 36CECh. 3 - (a) What kind of display is this? (b) Identify its...Ch. 3 - Prob. 38CECh. 3 - (a) What kind of display is this? (b) Identify its...Ch. 3 - (a) What kind of display is this? (b) Identify its...Ch. 3 - Prob. 41CECh. 3 - Prob. 42CECh. 3 - (a) Use Excel to prepare an appropriate type of...Ch. 3 - Prob. 44CECh. 3 - Prob. 45CECh. 3 - (a) Use Excel to prepare an appropriate type of...Ch. 3 - Prob. 47CECh. 3 - (a) Use Excel to prepare an appropriate type of...
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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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