Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter 19.3, Problem 3JC
To determine
Compute degrees of freedom for the
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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 19 Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
Ch. 19.3 - Why do we need the control group?Ch. 19.3 - Prob. 2JCCh. 19.3 - Prob. 3JCCh. 19.3 - Prob. 4JCCh. 19.3 - Prob. 5JCCh. 19.3 - Prob. 6JCCh. 19.4 - Prob. 7JCCh. 19.4 - Prob. 8JCCh. 19.4 - Prob. 9JCCh. 19 - Human births If there is no seasonal effect on...
Ch. 19 - Bank cards At a major credit card bank, the...Ch. 19 - Prob. 3ECh. 19 - Prob. 4ECh. 19 - Customer ages An analyst at a local bank wonders...Ch. 19 - Bank cards, once more A market researcher working...Ch. 19 - Human births, last time For the data in Exercise...Ch. 19 - Prob. 8ECh. 19 - Iliad injuries 800 BCE Homers Iliad is an epic...Ch. 19 - Prob. 10ECh. 19 - Prob. 11ECh. 19 - Prob. 12ECh. 19 - Dice After getting trounced by your little brother...Ch. 19 - MMs As noted in an earlier chapter, Mars Inc. says...Ch. 19 - Nuts A company says its premium mixture of nuts...Ch. 19 - Prob. 16ECh. 19 - NYPD and race Census data for New York City...Ch. 19 - Violence against women In its study When Men...Ch. 19 - Fruit flies Offspring of certain fruit flies may...Ch. 19 - Prob. 20ECh. 19 - Prob. 21ECh. 19 - Lottery numbers The fairness of the South African...Ch. 19 - Prob. 23ECh. 19 - Prob. 24ECh. 19 - Childbirth, part 2 In Exercise 23, the table shows...Ch. 19 - Prob. 26ECh. 19 - Prob. 27ECh. 19 - Prob. 28ECh. 19 - Prob. 29ECh. 19 - Does your doctor know? (part 4) In Exercises 24,...Ch. 19 - Prob. 31ECh. 19 - Prob. 32ECh. 19 - Prob. 33ECh. 19 - NYPD The table below shows the rank attained by...Ch. 19 - Prob. 35ECh. 19 - NYPD again Examine and comment on this table of...Ch. 19 - Cranberry juice Its common folk wisdom that...Ch. 19 - Prob. 38ECh. 19 - Montana A poll conducted by the University of...Ch. 19 - Fish diet Medical researchers followed 6272...Ch. 19 - Prob. 41ECh. 19 - Working parents In April 2009, Gallup published...Ch. 19 - Grades Two different professors teach an...Ch. 19 - Full moon Some people believe that a full moon...Ch. 19 - Grades, again In some situations where the...Ch. 19 - Full moon, next phase In Exercise 44, you found...Ch. 19 - Racial steering A subtle form of racial...Ch. 19 - Survival on the Titanic Newspaper headlines at the...Ch. 19 - Prob. 49ECh. 19 - Education by age Use the survey results in 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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