Aplia, 1 term Printed Access Card for Gravetter/Wallnau's Essentials of Statistics for the Behavioral Sciences, 8th
8th Edition
ISBN: 9781285079707
Author: Frederick J Gravetter, Larry B. Wallnau
Publisher: Cengage Learning
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Chapter 1.4, Problem 2LC
An English professor uses letter grades (A, B, C, D, and F) to evaluate a set of student essays. What kind of scale is being used to measure the quality of the essays?
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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
Aplia, 1 term Printed Access Card for Gravetter/Wallnau's Essentials of Statistics for the Behavioral Sciences, 8th
Ch. 1.2 - A researcher is interested in the texting habits...Ch. 1.2 - A researcher is interested in how watching a...Ch. 1.2 - Statistical techniques are classified into two...Ch. 1.2 - Briefly define the concept of sampling error.Ch. 1.3 - A research study comparing alcohol use for college...Ch. 1.3 - What two elements are necessary for a research...Ch. 1.3 - Stephens, Atkins, and Kingston (2009) conducted an...Ch. 1.4 - A tax form asks people to identify their annual...Ch. 1.4 - An English professor uses letter grades (A, B, C,...Ch. 1.4 - The teacher in a communications class asks...
Ch. 1.4 - A researcher studies the factors that determine...Ch. 1.4 - a. When measuring height to the nearest inch, what...Ch. 1.5 - Calculate each value requested for the following...Ch. 1.5 - Prob. 2LCCh. 1.5 - Use summation notation to express each of the...Ch. 1 - A researcher is investigating the effectiveness of...Ch. 1 - Define the terms population, sample, parameter,...Ch. 1 - Statistical methods arc classified into two major...Ch. 1 - Define the concept of sampling error and explain...Ch. 1 - Describe the data for a correlation research study...Ch. 1 - What is the goal for an experimental research...Ch. 1 - Knight and Haslam (2010) found that office workers...Ch. 1 - Judge and Cable (2010) found that thin women had...Ch. 1 - Two researchers are both interested in determining...Ch. 1 - Weinstein, McDermott, and Roediger (2010)...Ch. 1 - A research study reports that alcohol consumption...Ch. 1 - Oxytocin is a naturally occurring brain chemical...Ch. 1 - For each of the following, determine whether the...Ch. 1 - Four scales of measurement were introduced in this...Ch. 1 - In an experiment examining the effects Tai Chi on...Ch. 1 - Explain why shyness is a hypothetical construct...Ch. 1 - Ford and Torok (2008) found that motivational...Ch. 1 - For the following scores, find the value of each...Ch. 1 - For the following set of scores, find the value of...Ch. 1 - For the following set of scores, find the value of...Ch. 1 - Two scores, X and Y, are recorded for each of n =...Ch. 1 - Use summation notation to express each of the...Ch. 1 - Prob. 23P
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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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