A Problem Solving Approach To Mathematics For Elementary School Teachers, Loose Leaf Edition Plus Mylab Math With Pearson Etext -- 18 Week Access Card Package (13th Edition)
13th Edition
ISBN: 9780136209409
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott, Barbara Boschmans
Publisher: PEARSON
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Chapter 10, Problem 8NT
To determine
To create:
Set of data that ranges from 0 to 100, has a median 70, and an interquartile range 50.
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4. Assume that a risk-free money market account is added to the market described in Q3.
The continuously compounded rate of return on the money market account is log (1.1).
(i) For each given μ, use Lagrange multipliers to determine the proportions (as a
function of μ) of wealth invested in the three assets available for the minimum
variance portfolio with expected return μ.
(ii) Determine the market portfolio in this market and calculate its Sharp ratio.
3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free
asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05,
Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75.
(i) Given that an investor is targeting a total expected return of μ = 0.2. What
portfolio weights should they choose to meet this goal with minimum portfolio
variance? Correct all your calculations up to 4 decimal points.
(ii) Determine the global minimum-variance portfolio and the expected return and
variance of return of this portfolio (4 d.p.).
(iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient
frontier.
(iv) Without further calculation, explain how the minimum variance of the investor's
portfolio return will change if the two risky assets were independent.
2. A landlord is about to write a rental contract for a tenant which lasts T months. The
landlord first decides the length T > 0 (need not be an integer) of the contract, the
tenant then signs it and pays an initial handling fee of £100 before moving in. The
landlord collects the total amount of rent erT at the end of the contract at a continuously
compounded rate r> 0, but the contract stipulates that the tenant may leave before T,
in which case the landlord only collects the total rent up until the tenant's departure
time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r.
(i) Calculate the expected total payment EW the landlord will receive in terms of T.
(ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides
that the rental rate r should depend on the contract length T by
r(T)
=
λ
√T
1
For each given λ, what T (as a function of X) should the landlord choose so as to
maximise their expected utility? Justify your answer.
Hint. It might be…
Chapter 10 Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers, Loose Leaf Edition Plus Mylab Math With Pearson Etext -- 18 Week Access Card Package (13th Edition)
Ch. 10.1 - Suggest how students at different grades might...Ch. 10.1 - Mathematical Connections What are the Nielsen...Ch. 10.1 - Prob. 4MCCh. 10.1 - Read about basic ideas of statistics in Common...Ch. 10.1 - National Assessment of Educational ProgressNAEP...Ch. 10.1 - Prob. 2NAEPCh. 10.1 - Prob. 3NAEPCh. 10.1A - If one wanted to study the effect of using a...Ch. 10.1A - Prob. 2ACh. 10.1A - Prob. 3A
Ch. 10.1A - Prob. 4ACh. 10.1A - Prob. 5ACh. 10.1A - Prob. 6ACh. 10.1A - A second-grade class has a project to determine...Ch. 10.1A - Prob. 8ACh. 10.1A - Prob. 9ACh. 10.1A - Decide whether each of the following questions is...Ch. 10.1A - Prob. 11ACh. 10.1A - If a class were to investigate how many countries...Ch. 10.1A - Prob. 13ACh. 10.1A - In a set of student evaluations of their...Ch. 10.1A - If a bar graph like the one shown here were used...Ch. 10.1A - Prob. 16ACh. 10.1B - Assessment To study the effect of student...Ch. 10.1B - Assessment If students are measuring a tablespoon...Ch. 10.1B - Assessment If third graders were measuring an...Ch. 10.1B - Assessment To determine student computer use,...Ch. 10.1B - Suppose a poll is to be conducted in an elementary...Ch. 10.1B - Determine the population and the sample in the...Ch. 10.1B - A second-grade class has a project to determine...Ch. 10.1B - An elementary school class decides to determine...Ch. 10.1B - Prob. 12ACh. 10.1B - Prob. 13ACh. 10.1B - Assessment A university professor used a rating...Ch. 10.1B - Prob. 15ACh. 10.2 - Mathematical Connections a. Discuss when a...Ch. 10.2 - Mathematical Connections Explain whether a circle...Ch. 10.2 - Mathematical Connections Explain why the sum of...Ch. 10.2 - Mathematical Connections The federal budget for...Ch. 10.2 - Mathematical Connections Tell whether it is...Ch. 10.2 - Mathematical Connections Car sales from 1990 to...Ch. 10.2 - Mathematical Connections Find five examples of...Ch. 10.2 - Mathematical Connections A graph similar to the...Ch. 10.2 - Mathematical Connections Vale asks whether a stem...Ch. 10.2 - Mathematical Connections A histogram of the data...Ch. 10.2 - Mathematical Connections Paul asks how to create a...Ch. 10.2 - Mathematical Connections On the School Book Page...Ch. 10.2 - Prob. 15MCCh. 10.2 - Answer the Try It on the School Book Page on page...Ch. 10.2 - Answer the Try It on the School Book Page on page...Ch. 10.2 - National Assessment of Educational Progress NAEP...Ch. 10.2 - National Assessment of Educational Progress NAEP...Ch. 10.2 - National Assessment of Educational Progress NAEP...Ch. 10.2 - National Assessment of Educational Progress NAEP...Ch. 10.2 - National Assessment of Educational Progress NAEP...Ch. 10.2A - The following the pictograph shows the approximate...Ch. 10.2A - Prob. 2ACh. 10.2A - Prob. 3ACh. 10.2A - Sixth grade students reported the numbers of apps...Ch. 10.2A - Prob. 5ACh. 10.2A - Prob. 6ACh. 10.2A - Prob. 7ACh. 10.2A - Prob. 8ACh. 10.2A - Prob. 9ACh. 10.2A - Prob. 10ACh. 10.2A - Prob. 11ACh. 10.2A - Prob. 12ACh. 10.2A - Prob. 13ACh. 10.2A - a. A 2-inch-long rectangle serves as a percentage...Ch. 10.2A - Seniors Sierra High were asked to about their...Ch. 10.2A - Prob. 16ACh. 10.2A - Prob. 17ACh. 10.2A - Prob. 18ACh. 10.2B - The following pictograph shows the approximate...Ch. 10.2B - Display the following information about the status...Ch. 10.2B - In the figure shown, monthly sales of three...Ch. 10.2B - Prob. 4ACh. 10.2B - A list of presidents, with the number of children...Ch. 10.2B - Prob. 6ACh. 10.2B - The heights reached by 15 model rockets launched...Ch. 10.2B - Prob. 8ACh. 10.2B - Given the following bar graph, estimate the length...Ch. 10.2B - Prob. 10ACh. 10.2B - Prob. 11ACh. 10.2B - The graph below shows the number of books read by...Ch. 10.2B - Prob. 13ACh. 10.2B - Use the circle graph to answer the following...Ch. 10.2B - a. In a circle graph, a sector containing 82...Ch. 10.2B - A percentage bar graph with 100 is drawn to depict...Ch. 10.2B - Prob. 17ACh. 10.2B - Prob. 18ACh. 10.3 - Explain the concept of association as it is...Ch. 10.3 - Jacquie argued that scatterplots had little value...Ch. 10.3 - Prob. 6MCCh. 10.3 - The Garcia family drew a circle graph of their...Ch. 10.3 - Prob. 9MCCh. 10.3 - Prob. 10MCCh. 10.3 - A teacher surveyed 8 students in a class to find...Ch. 10.3 - Prob. 2NAEPCh. 10.3A - Assessment The graph below shows the population of...Ch. 10.3A - Assessment The graph shows the number of snow...Ch. 10.3A - Assessment The graph shows the US rates of adult...Ch. 10.3A - Prob. 5ACh. 10.3A - Prob. 6ACh. 10.3A - Prob. 7ACh. 10.3A - Assessment Consider an arithmetic sequence with...Ch. 10.3A - Prob. 9ACh. 10.3A - Assessment In the following scatterplots, find an...Ch. 10.3A - Assessment The following data show the amount of...Ch. 10.3A - Assessment If a trend line has equation...Ch. 10.3A - Assessment If a trend line has equation y=150.8x,...Ch. 10.3A - Assessment For each of the following pairs of...Ch. 10.3B - Prob. 1ACh. 10.3B - Prob. 2ACh. 10.3B - Prob. 3ACh. 10.3B - Prob. 4ACh. 10.3B - Prob. 5ACh. 10.3B - Prob. 6ACh. 10.3B - Prob. 7ACh. 10.3B - Prob. 8ACh. 10.3B - Prob. 9ACh. 10.3B - Prob. 10ACh. 10.3B - Prob. 11ACh. 10.3B - Prob. 12ACh. 10.3B - Prob. 13ACh. 10.3B - Assessment If a trend line has equation...Ch. 10.3B - Assessment For each of the following pairs of...Ch. 10.4 - Mathematical Connections Karl had scores of...Ch. 10.4 - The mean of the five numbers given is 50: 20 35 50...Ch. 10.4 - Prob. 6MCCh. 10.4 - Mathematical Connections Explain why the mode...Ch. 10.4 - Prob. 8MCCh. 10.4 - Mathematical Connections The mean of 5,7,9 is 7....Ch. 10.4 - Mathematical Connections If each number in a set...Ch. 10.4 - Mathematical Connections What does a large...Ch. 10.4 - Mathematical Connections In each pair of variables...Ch. 10.4 - Mathematical Connections Use the data in the...Ch. 10.4 - Mathematical Connections A student asks, If the...Ch. 10.4 - Mathematical Connections Jose asks, Why can a...Ch. 10.4 - Mathematical Connections Suppose the class takes a...Ch. 10.4 - Mathematical Connections A student asks if it is...Ch. 10.4 - Prob. 19MCCh. 10.4 - Mathematical Connections A student asks if it is...Ch. 10.4 - Mathematical Connections Mels mean on 10 tests for...Ch. 10.4 - Mathematical Connections On the School Book Page,...Ch. 10.4 - Prob. 25MCCh. 10.4 - Mathematical Connections Given the bar graph...Ch. 10.4 - Mathematical Connections Refer to the following...Ch. 10.4 - Mathematical Connections Following are raw test...Ch. 10.4 - Josephs current test scores, in points, are 83,...Ch. 10.4 - National Assessment of Educational Progress NAEP...Ch. 10.4 - Prob. 3NAEPCh. 10.4 - Richard wants to estimate the average mean monthly...Ch. 10.4A - Assessment Calculate the mean, the median, and the...Ch. 10.4A - Prob. 2ACh. 10.4A - Assessment a. If three students scored 75 on a...Ch. 10.4A - Prob. 4ACh. 10.4A - Assessment Suppose in Selinas class there were...Ch. 10.4A - Prob. 6ACh. 10.4A - Prob. 7ACh. 10.4A - Prob. 8ACh. 10.4A - Prob. 9ACh. 10.4A - Prob. 10ACh. 10.4A - Prob. 11ACh. 10.4A - Assessment The city of Podunk advertised itself as...Ch. 10.4A - Prob. 13ACh. 10.4A - Prob. 14ACh. 10.4A - Prob. 15ACh. 10.4A - Assessment Following are box plots comparing the...Ch. 10.4A - Prob. 17ACh. 10.4A - Assessment The following table shows the heights...Ch. 10.4A - Assessment What is the standard deviation of the...Ch. 10.4A - Prob. 20ACh. 10.4A - Prob. 21ACh. 10.4A - Assessment The average phone call in a certain...Ch. 10.4A - Prob. 23ACh. 10.4A - Prob. 24ACh. 10.4A - Prob. 25ACh. 10.4A - Prob. 26ACh. 10.4A - Prob. 27ACh. 10.4A - Prob. 28ACh. 10.4B - Calculate the mean, the median, and the mode for...Ch. 10.4B - Prob. 2ACh. 10.4B - Prob. 3ACh. 10.4B - Prob. 4ACh. 10.4B - Prob. 5ACh. 10.4B - Prob. 6ACh. 10.4B - Prob. 7ACh. 10.4B - Prob. 9ACh. 10.4B - Prob. 10ACh. 10.4B - Prob. 11ACh. 10.4B - Prob. 12ACh. 10.4B - Prob. 13ACh. 10.4B - Prob. 14ACh. 10.4B - Ginnys median score on three tests was 90. Her...Ch. 10.4B - Prob. 16ACh. 10.4B - Prob. 17ACh. 10.4B - The following table shows the heights in feet of...Ch. 10.4B - a. If all the numbers in a set are equal, what is...Ch. 10.4B - In a school system, teachers start at a salary of...Ch. 10.4B - Prob. 21ACh. 10.4B - Prob. 22ACh. 10.4B - Prob. 23ACh. 10.4B - Prob. 24ACh. 10.4B - The weights of newborn babies in a certain country...Ch. 10.4B - Prob. 26ACh. 10.4B - Prob. 27ACh. 10.4B - Prob. 28ACh. 10.4B - Prob. 29ACh. 10.CR - Suppose you read that the average family in...Ch. 10.CR - Prob. 2CRCh. 10.CR - Prob. 3CRCh. 10.CR - Prob. 5CRCh. 10.CR - Prob. 6CRCh. 10.CR - The budget for the Wegetem Crime Co. is 2,000,000....Ch. 10.CR - Prob. 8CRCh. 10.CR - Prob. 9CRCh. 10.CR - Prob. 11CRCh. 10.CR - Prob. 12CRCh. 10.CR - Prob. 13CRCh. 10.CR - Prob. 14CRCh. 10.CR - CHAPTER 10 REVIEW The following chart lists the...Ch. 10.CR - Prob. 16CRCh. 10.CR - Prob. 17CRCh. 10.CR - Prob. 19CRCh. 10.CR - Prob. 20CRCh. 10.CR - Prob. 21CRCh. 10.CR - Prob. 22CRCh. 10.CR - Prob. 24CRCh. 10.CR - CHAPTER 10 REVIEW Following are the record...Ch. 10.CR - Prob. 26CRCh. 10.CR - Prob. 27CRCh. 10.CR - Prob. 28CRCh. 10.CR - Prob. 29CRCh. 10.CR - Prob. 30CRCh. 10.CR - Prob. 32CRCh. 10.CR - CHAPTER 10 REVIEW Give examples of several ways to...Ch. 10.CR - Prob. 34CRCh. 10.CR - Prob. 35CRCh. 10.CR - Prob. 36CRCh. 10.CR - Prob. 37CRCh. 10 - Prob. 1NTCh. 10 - Prob. 2NTCh. 10 - Prob. 4NTCh. 10 - Prob. 5NTCh. 10 - Prob. 6NTCh. 10 - Prob. 7NTCh. 10 - Prob. 8NT
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- Please solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forwardPlease ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward
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