Introductory Statistics
3rd Edition
ISBN: 9780135188927
Author: Gould, Robert, Ryan, Colleen N. (colleen Nooter)
Publisher: Pearson,
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Chapter 10, Problem 67CRE
To determine
Determine whether the data given in the table is appropriate to conduct a chi-square test to test whether or not the ethnic breakdown of the military is the same as the ethnic distribution of the U.S. population.
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solve the question based on hw 1, 1.41
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…
Chapter 10 Solutions
Introductory Statistics
Ch. 10 - Tests a. In Chapter 8, you learned some tests of...Ch. 10 - In Chapter 9, you learned some tests of means. Are...Ch. 10 - Crime and Gender A statistics student conducted a...Ch. 10 - Red Cars and Stop Signs The table shows the raw...Ch. 10 - The table summarizes the outcomes of a study that...Ch. 10 - Finger Length There is a theory that relative...Ch. 10 - Student Loans-California According to a 2017...Ch. 10 - Student Loans-Illinois According to a 2017 report,...Ch. 10 - Breakfast Habits (Example 1 2) In a 2015 study by...Ch. 10 - Fast Food Habits In the study referenced in...
Ch. 10 - Mummies with Heart Disease According to the...Ch. 10 - Texting While Driving According to the 2015 High...Ch. 10 - Violins Stradivarius violins, made in the 1700s by...Ch. 10 - Coin Flips You flip a coin 100 times and get 58...Ch. 10 - Prob. 15SECh. 10 - Prob. 16SECh. 10 - Are Humans Like Random Number Generators? (Example...Ch. 10 - Is the Random Number Table Really Random? We...Ch. 10 - Coin Spins A penny was spun on a hard, flat...Ch. 10 - Internet Usage In 2018 Pew Research reported that...Ch. 10 - Dreidel Spinning When playing Dreidel, (see photo)...Ch. 10 - Plastic Dreidel See exercise 10.21 for an...Ch. 10 - Is the Six-Sided Die Fair? The table shows the...Ch. 10 - Is the Six-Sided Die Fair? Repeat the chi-square...Ch. 10 - Violins Professional musicians listened to five...Ch. 10 - Mummies with Heart Disease Exercise 10.11 on...Ch. 10 - Party and Right Direction (Example 4) Suppose a...Ch. 10 - Antibiotic or Placebo A large number of surgery...Ch. 10 - Relevant Education (Example 5) A 2018 Gallup poll...Ch. 10 - Prob. 30SECh. 10 - Fitness The table shows the percentage of all men...Ch. 10 - Food Security The table shows the percentage of...Ch. 10 - Fitness App Use and Gender (Example 6) In a 2015...Ch. 10 - Diet App Use and Gender In the study referenced in...Ch. 10 - HPV Vaccination Rates A vaccine is available to...Ch. 10 - HPV Vaccine Literacy Rates In the study described...Ch. 10 - Gender and Happiness of Marriage The table shows...Ch. 10 - Is Smiling Independent of Age? Randomly chosen...Ch. 10 - Preschool Attendance and High School Graduation...Ch. 10 - Preschool Attendance and High School Graduation...Ch. 10 - Preschool Attendance and High School Graduation...Ch. 10 - Prob. 42SECh. 10 - Prob. 43SECh. 10 - Marijuana Legalization The 2018 Pew Research poll...Ch. 10 - Brain Bleed Treatment In a 2018 article published...Ch. 10 - Multiple Sclerosis Treatment In a 2018 article...Ch. 10 - Prob. 47SECh. 10 - Political Party Affiliation and Generation A 2018...Ch. 10 - Prob. 49SECh. 10 - Night Shifts A random sample of nurses working...Ch. 10 - Gender and Political Party Affiliation The data in...Ch. 10 - Children and Happiness The data in the table come...Ch. 10 - Prob. 53SECh. 10 - Nice Rats Rats had a choice of freeing another rat...Ch. 10 - Peanut Allergies In a 2015 study reported in the...Ch. 10 - Peanut Allergies In the study described in...Ch. 10 - Prob. 57CRECh. 10 - In exercises 10.57 to 10.64, choose an appropriate...Ch. 10 - Prob. 59CRECh. 10 - Prob. 60CRECh. 10 - Prob. 61CRECh. 10 - In exercises 10.57 to 10.64, choose an appropriate...Ch. 10 - Prob. 63CRECh. 10 - In exercises 10.57 to 10.64, choose an appropriate...Ch. 10 - Perry Preschool Arrests The Perry Preschool...Ch. 10 - Parental Training and Criminal Behavior of...Ch. 10 - Prob. 67CRECh. 10 - Prob. 68CRECh. 10 - Harassment in the Workplace An 2017 NPR/Marist...Ch. 10 - Prob. 70CRECh. 10 - Robot Cockroaches Cockroaches tend to rest in...Ch. 10 - Robot Cockroaches Refer to the description in...Ch. 10 - Prob. 73CRECh. 10 - Conviction Rate with Opposite Race Here are the...
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- Negate the following compound statement using De Morgans's laws.arrow_forwardNegate 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_forward
- Negate the following compound statement using De Morgans's laws.arrow_forwardCharacterize (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_forward
- Prove 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_forwardLet 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_forward
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