Stats
5th Edition
ISBN: 9780135163825
Author: De Veaux, Richard D., Velleman, Paul F., BOCK, David E.
Publisher: Pearson,
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Chapter 11, Problem 16E
a.
To determine
Check whether the given study is an experimental study.
Find the type of the given study.
b.
To determine
Explain the reason for the inappropriateness of the interpretation that “The shorter men are at higher risk of dying from a heart attack”.
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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 11 Solutions
Stats
Ch. 11.3 - 1. At one time, a method called “gastric freezing”...Ch. 11.4 - Prob. 2JCCh. 11 - Prob. 1ECh. 11 - 2. E-commerce A business student conjectures that...Ch. 11 - 3. Tips A pizza delivery driver, always trying to...Ch. 11 - 4. Tomatoes You want to compare the tastiness and...Ch. 11 - 5. Tips II For the experiment described in...Ch. 11 - 6. Tomatoes II For the experiment described in...Ch. 11 - 7. Tips again For the experiment of Exercise 3,...Ch. 11 - 8. Tomatoes again For the experiment of Exercise...
Ch. 11 - 9. More tips Is the experiment of Exercise 3...Ch. 11 - 10. More tomatoes If the tomato taster doesn’t...Ch. 11 - 11. Block that tip The driver of Exercise 3 wants...Ch. 11 - 12. Blocking tomatoes To obtain enough plants for...Ch. 11 - 13. Confounded tips For the experiment of Exercise...Ch. 11 - 14. Tomatoes finis What factors might confound the...Ch. 11 - 15. Standardized test scores For his statistics...Ch. 11 - 16. Heart attacks and height Researchers who...Ch. 11 - 17. MS and vitamin D Multiple sclerosis (MS) is an...Ch. 11 - 18. Super Bowl commercials When spending large...Ch. 11 - Prob. 19ECh. 11 - 20. Honesty Coffee stations in offices often just...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 21–34. What’s the design? Read each brief report...Ch. 11 - 35. Omega-3 Exercise 21 describes an experiment...Ch. 11 - 36. Insomnia Exercise 24 describes an experiment...Ch. 11 - 37. Omega-3, revisited Exercises 21 and 35...Ch. 11 - 38. Insomnia, again Exercises 24 and 36 describe...Ch. 11 - 39. Omega-3, finis Exercises 21, 35, and 37...Ch. 11 - 40. Insomnia, at last Exercises 24, 36, and 38...Ch. 11 - 41. Injuries Exercise 33 describes an experiment...Ch. 11 - 42. Tomatoes II Describe a strategy to randomly...Ch. 11 - 43. Shoes A running-shoe manufacturer wants to...Ch. 11 - 44. Swimsuits A swimsuit manufacturer wants to...Ch. 11 - 45. Hamstrings Exercise 33 discussed an experiment...Ch. 11 - 46. Diet and blood pressure An experiment showed...Ch. 11 - Prob. 47ECh. 11 - 48. Contrast baths Contrast bath treatments use...Ch. 11 - 49. Wine A Danish study published in the Archives...Ch. 11 - 50. Swimming Recently, a group of adults who swim...Ch. 11 - 51. Dowsing Before drilling for water, many rural...Ch. 11 - 52. Healing A medical researcher suspects that...Ch. 11 - 53. Reading Some schools teach reading using...Ch. 11 - 54. Gas mileage Do cars get better gas mileage...Ch. 11 - 55. Weekend deaths A study published in the New...Ch. 11 - 56. Shingles A research doctor has discovered a...Ch. 11 - 57. Beetles Hoping to learn how to control crop...Ch. 11 - 58. SAT prep Can special study courses actually...Ch. 11 - 59. Safety switch An industrial machine requires...Ch. 11 - 60. Washing clothes A consumer group wants to test...Ch. 11 - 61. Skydiving, anyone? A humor piece published in...
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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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