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 12, Problem 5E
Wardrobe In your dresser are five blue shirts, three red shirts, and two black shirts.
- a) What is the
probability of randomly selecting a red shirt? - b) What is the probability that a randomly selected shirt is not black?
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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
Intro Stats, Books a la Carte Edition (5th Edition)
Ch. 12.1 - One common proposal for beating the lottery is to...Ch. 12.3 - We sampled some pages of this book at random to...Ch. 12.3 - Prob. 3JCCh. 12.5 - Prob. 4JCCh. 12.6 - Prob. 5JCCh. 12 - Flipping a coin Flipping a fair coin is said to...Ch. 12 - Dice Rolling a fair six-sided die is supposed to...Ch. 12 - Flipping a coin II Your friend says: I flipped...Ch. 12 - Dice II After rolling doubles on a pair of dice...Ch. 12 - Wardrobe In your dresser are five blue shirts,...
Ch. 12 - Prob. 6ECh. 12 - Cell phones and surveys A 2015 study conducted by...Ch. 12 - Cell phones and surveys II The survey by the...Ch. 12 - Pet ownership Suppose that 25% of people have a...Ch. 12 - Cooking and shopping Forty-five percent of...Ch. 12 - Sports What is the probability that a person likes...Ch. 12 - Sports again From Exercise 11, if someone doesnt...Ch. 12 - Late to the train A student figures that he has a...Ch. 12 - Field goals A nervous kicker usually makes 70% of...Ch. 12 - Titanic On the Titanic, the probability of...Ch. 12 - Prob. 16ECh. 12 - Facebook Facebook reports that 70% of its users...Ch. 12 - Prob. 18ECh. 12 - Prob. 19ECh. 12 - Prob. 20ECh. 12 - Prob. 21ECh. 12 - Online banking last time Given the probabilities...Ch. 12 - Sample spaces For each of the following, list the...Ch. 12 - Sample spaces II For each of the following, list...Ch. 12 - Prob. 25ECh. 12 - Rain The weather reporter on TV makes predictions...Ch. 12 - Winter Comment on the following quotation: What I...Ch. 12 - Snow After an unusually dry autumn, a radio...Ch. 12 - Auto insurance Insurance companies collect annual...Ch. 12 - Prob. 30ECh. 12 - Prob. 31ECh. 12 - Prob. 32ECh. 12 - Electronics Suppose that 46% of families living in...Ch. 12 - Homes Funding for many schools comes from taxes...Ch. 12 - Prob. 35ECh. 12 - Lefties Although its hard to be definitive in...Ch. 12 - Prob. 37ECh. 12 - Prob. 38ECh. 12 - Car repairs A consumer organization estimates that...Ch. 12 - Stats projects In a large Introductory statistics...Ch. 12 - More repairs Consider again the auto repair rates...Ch. 12 - Another project You are assigned to be part of a...Ch. 12 - Prob. 43ECh. 12 - Final project You used the Multiplication Rule to...Ch. 12 - Prob. 45ECh. 12 - Polling, part II According to Pew Research, the...Ch. 12 - Prob. 47ECh. 12 - Blood The American Red Cross says that about 45%...Ch. 12 - Prob. 49ECh. 12 - Disjoint or independent? In Exercise 48, you...Ch. 12 - Prob. 51ECh. 12 - The train To get to work, a commuter must cross...Ch. 12 - Prob. 53ECh. 12 - Pepsi For a sales promotion, the manufacturer...Ch. 12 - 9/11? On September 11, 2002, the first anniversary...Ch. 12 - Prob. 56ECh. 12 - Prob. 57ECh. 12 - Prob. 58ECh. 12 - Health The probabilities that an adult American...Ch. 12 - Immigration The table shows the political...Ch. 12 - Prob. 61ECh. 12 - Birth order, take 2 Look again at the data about...Ch. 12 - Batteries A junk box in your room contains a dozen...Ch. 12 - Prob. 64ECh. 12 - Eligibility A university requires its biology...Ch. 12 - Benefits Fifty-six percent of all American workers...Ch. 12 - Unsafe food Early in 2010, Consumer Reports...Ch. 12 - Prob. 68ECh. 12 - Prob. 69ECh. 12 - Politics Given the table of probabilities from...Ch. 12 - Gender A poll conducted by Gallup classified...Ch. 12 - Cars A random survey of autos parked in student...Ch. 12 - Prob. 73ECh. 12 - Prob. 74ECh. 12 - Late luggage Remember Leah (Exercise 73)? Suppose...Ch. 12 - Prob. 76ECh. 12 - Prob. 77ECh. 12 - Prob. 78ECh. 12 - Prob. 79ECh. 12 - Prob. 80ECh. 12 - Drunks Police often set up sobriety...Ch. 12 - No-shows An airline offers discounted...Ch. 12 - Prob. 83ECh. 12 - Parts A company manufacturing electronic...Ch. 12 - HIV testing In July 2005, the journal Annals of...Ch. 12 - Polygraphs Lie detectors are controversial...
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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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