EBK STATISTICS FOR BUSINESS & ECONOMICS
12th Edition
ISBN: 8220100460463
Author: Anderson
Publisher: CENGAGE L
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Textbook Question
Chapter 21.3, Problem 8E
Consider a variation of the PDC decision tree shown in Figure 21.5. The company must first decide whether to undertake the market research study. If the market research study is conducted, the outcome will either be favorable (F) or unfavorable (U). Assume there are only two decision alternatives d1 and d2 and two states of nature s1 and s2. The payoff table showing profit is as follows:
| State of Nature | ||
| Decision Alternative | s1 | s2 |
| d1 | 100 | 300 |
| d2 | 400 | 200 |
- a. Show the decision tree.
- b. Use the following probabilities. What is the optimal decision strategy?
| P(F) = .56 | P(s1 | F) = .57 | P(s1 | U) = .18 | P(s1) = .40 |
| P(U) = .44 | P(s2 | F) = .43 | P(s2 | U) = .82 | P(s2) = .60 |
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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 21 Solutions
EBK STATISTICS FOR BUSINESS & ECONOMICS
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