ESSEN OF BUSINESS ANALYTICS (LL) BOM
2nd Edition
ISBN: 9781337128629
Author: Camm
Publisher: CENGAGE L
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Chapter 3, Problem 18P
The Ajax Company uses a portfolio approach to manage their research and development (R&D) projects. Ajax wants to keep a mix of projects to balance the expected return and risk profiles of their R&D activities. Consider a situation in which Ajax has six R&D projects as characterized in the table. Each project is given an expected rate of return and a risk assessment, which is a value between 1 and 10, where 1 is the least risky and 10 is the most risky. Ajax would like to visualize their current R&D projects to keep track of the overall risk and return of their R&D portfolio.
- a. Create a bubble chart in which the expected rate of return is along the horizontal axis, the risk estimate is on the vertical axis, and the size of the bubbles represents the amount of capital invested. Format this chart for best presentation by adding axis labels and labeling each bubble with the project number.
- b. The efficient frontier of R&D projects represents the set of projects that have the highest expected rate of return for a given level of risk. In other words, any project that has a smaller expected rate of return for an equivalent, or higher, risk estimate cannot be on the efficient frontier. From the bubble chart in part a, which projects appear to be located on the efficient frontier?
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1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
In a town with 5000 adults, a sample of 50 is selected using SRSWOR and asked their opinion of a proposed municipal project; 30 are found to favor it and 20 oppose it. If, in fact, the adults of the town were equally divided on the proposal, what would be the probability of observing what has been observed? Approximate using the Binomial distribution. Compare this with the exact probability which is 0.0418.
Chapter 3 Solutions
ESSEN OF BUSINESS ANALYTICS (LL) BOM
Ch. 3 - A sales manager is trying to determine appropriate...Ch. 3 - The following table shows an example of gross...Ch. 3 - The following table provides monthly revenue...Ch. 3 - In the file MajorSalary, data have been collected...Ch. 3 - Entrepreneur magazine ranks franchises. Among the...Ch. 3 - The file MutualFunds contains a data set with...Ch. 3 - The file TaxData contains information from federal...Ch. 3 - The file FDICBankFailures contains data on...Ch. 3 - The following 20 observations are for two...Ch. 3 - The file Fortune500 contains data for profits and...
Ch. 3 - The International Organization of Motor Vehicle...Ch. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - The total number of term life insurance contracts...Ch. 3 - An automotive company is considering the...Ch. 3 - Consider the following survey results regarding...Ch. 3 - The Northwest regional manager of Logan Outdoor...Ch. 3 - The Ajax Company uses a portfolio approach to...Ch. 3 - Heat maps can be very useful for identifying...Ch. 3 - The following table shows monthly revenue for six...Ch. 3 - Prob. 21PCh. 3 - Aurora Radiological Services is a health care...Ch. 3 - The motion picture industry is an extremely...
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