Essentials Of Business Analytics
1st Edition
ISBN: 9781285187273
Author: Camm, Jeff.
Publisher: Cengage Learning,
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Chapter 12, Problem 2P
Southland Corporation’s decision to produce a new line of recreational products resulted in the need to construct either a small plant or a large plant. The best selection of plant size depends on how the marketplace reacts to the new product line. To conduct an analysis, marketing management has decided to view the possible long-run demand as low, medium, or high. The following payoff table shows the projected profit in millions of dollars:
- a. What is the decision to be made, and what is the chance
event for Southland’s problem? - b. Construct a decision tree.
- c. Recommend a decision based on the use of the optimistic, conservative, and minimax regret approaches.
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3. Prove that, for any random variable X, the minimum of E(X - a)² is attained
for a = EX.
Proved
7. Cantelli's inequality. Let X be a random variable with finite variance, o².
(a) Prove that, for x ≥ 0,
P(X EX2x)≤
02
x² +0²
202
P(|X - EX2x)<≤
(b) Find X assuming two values where there is equality.
(c) When is Cantelli's inequality better than Chebyshev's inequality?
(d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall,
from Proposition 6.1, that an application of Chebyshev's inequality yields
the bound o√√2.
(e) Generalize Cantelli's inequality to moments of order r 1.
The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.
Chapter 12 Solutions
Essentials Of Business Analytics
Ch. 12 - Prob. 1PCh. 12 - Southland Corporation’s decision to produce a new...Ch. 12 - Amy Lloyd is interested in leasing a new Honda and...Ch. 12 - Investment advisors estimated the stock market...Ch. 12 - Hudson Corporation is considering three options...Ch. 12 - Prob. 6PCh. 12 - Myrtle Air Express decided to offer direct service...Ch. 12 - Video Tech is considering marketing one of two new...Ch. 12 - Seneca Hill Winery recently purchased land for the...Ch. 12 - Hemmingway, Inc. is considering a $5 million...
Ch. 12 - The following profit payoff table was presented in...Ch. 12 - Suppose that you are given a decision situation...Ch. 12 - A firm has three investment alternatives. Payoffs...Ch. 12 - Alexander Industries is considering purchasing an...Ch. 12 - In a certain state lottery, a lottery ticket costs...Ch. 12 - Three decision makers have assessed utilities for...Ch. 12 - In Problem 22, if P(s1) = 0.25, P(s2) = 0.50, and...Ch. 12 - Translate the following monetary payoffs into...Ch. 12 - Consider a decision maker who is comfortable with...
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