Student Solutions Manual for Brase/Brase's Understanding Basic Statistics, 7th
7th Edition
ISBN: 9781305258792
Author: BRASE, Charles Henry
Publisher: Cengage Learning
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Chapter 1.1, Problem 15P
Critical Thinking You are interested in the weights of backpacks students carry to class and decide to conduct a study using the backpacks carried by 30 students.
(a) Give some instructions for weighing the backpacks. Include unit of measure, accuracy of measure, and type of scale.
(b) Do you think each student asked will allow you to weigh his or her backpack?
(c) Do you think telling students ahead of time that you are going to weigh their backpacks will make a difference in the weights?
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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 1 Solutions
Student Solutions Manual for Brase/Brase's Understanding Basic Statistics, 7th
Ch. 1.1 - Statistical Literacy In a statistical study, what...Ch. 1.1 - Statistical Literacy Are data at the nominal level...Ch. 1.1 - Statistical Literacy What is the difference...Ch. 1.1 - Statistical Literacy For a set population, does a...Ch. 1.1 - Critical Thinking Numbers are often assigned to...Ch. 1.1 - Interpretation Lucy conducted a survey asking some...Ch. 1.1 - Marketing: Fast Food A national survey asked 1261...Ch. 1.1 - Advertising: Auto Mileage What is the average...Ch. 1.1 - Ecology: Wetlands Government agencies carefully...Ch. 1.1 - Archaeology: Ireland The archaeological site of...
Ch. 1.1 - Student Life: Levels of Measurement Categorize...Ch. 1.1 - Business: Levels of Measurement Categorize these...Ch. 1.1 - Fishing: Levels of Measurement Categorize these...Ch. 1.1 - Education: Teacher Evaluation If you were going to...Ch. 1.1 - Critical Thinking You are interested in the...Ch. 1.2 - Statistical Literacy Explain the difference...Ch. 1.2 - Statistical Literacy Explain the difference...Ch. 1.2 - Statistical Literacy Marcie conducted a study of...Ch. 1.2 - Statistical Literacy A random sample of students...Ch. 1.2 - Interpretation In a random sample of 50 students...Ch. 1.2 - Interpretation A campus performance series...Ch. 1.2 - Critical Thinking Greg took a random sample of...Ch. 1.2 - Critical Thinking Consider the students in your...Ch. 1.2 - Critical Thinking Suppose you are assigned the...Ch. 1.2 - Critical Thinking In each of the following...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Prob. 14PCh. 1.2 - Computer Simulation: Roll of a Die A die is a cube...Ch. 1.2 - Prob. 16PCh. 1.2 - Education: Test Construction Professor Gill is...Ch. 1.2 - Education: Test Construction Professor Gill uses...Ch. 1.2 - Sampling Methods: Benefits Package An important...Ch. 1.2 - Sampling Methods: Health Care Modern Managed...Ch. 1.3 - Prob. 1PCh. 1.3 - Statistical Literacy Consider a completely...Ch. 1.3 - Critical Thinking A brief survey regarding...Ch. 1.3 - Critical Thinking A randomized block design was...Ch. 1.3 - Interpretation Zane is examining two studies...Ch. 1.3 - Prob. 6PCh. 1.3 - Ecology: Gathering Data Which technique for...Ch. 1.3 - General: Gathering Data Which technique for...Ch. 1.3 - General: Completely Randomized Experiment How...Ch. 1.3 - Survey: Manipulation The NewYork Times did a...Ch. 1.3 - Critical Thinking An agricultural study is...Ch. 1 - Critical Thinking Sudoku is a puzzle consisting of...Ch. 1 - Critical Thinking Alisha wants to do a statistical...Ch. 1 - Statistical Literacy You are conducting a study of...Ch. 1 - Radio Talk Show: Sample Bias A radio talk show...Ch. 1 - Prob. 5CRCh. 1 - General: Type of Sampling Categorize the type of...Ch. 1 - General: Gathering Data Which technique fur...Ch. 1 - General: Experiment How would you use a completely...Ch. 1 - Student Life: Data Collection Project Make a...Ch. 1 - Form Problem: Fireflies Suppose you air conducting...Ch. 1 - Prob. 1DHGPCh. 1 - Use a random-number table or random-number...Ch. 1 - What does it mean to say that we are going to use...Ch. 1 - In your own words, explain the differences among...Ch. 1 - Simulate the results of tossing a fair die 18...Ch. 1 - Prob. 2UTA
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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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