Statistical Techniques in Business and Economics
18th Edition
ISBN: 9781260579611
Author: Douglas Lind; William Marchal; Samuel Wathen
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 20, Problem 1SR
To determine
Prove that the expected payoff for the act of purchasing Rim Homes stock is $1,760.
Expert Solution & Answer
Answer to Problem 1SR
The expected payoff for the act of purchasing Rim Homes stock is $1,760.
Explanation of Solution
From the Table 20-1, the bull market and bear stock for the Rim homes are 2,200 and 1,100, respectively. The corresponding probabilities are 0.60 and 0.40.
The expected payoff for the act of purchasing Rim Homes stock is calculated as follows:
| Payoff value | Probability | Expected value | |
| Bull market | 2,200 | 0.60 | |
| Bear market | 1,100 | 0.40 | |
Then, the expected payoff for the act of purchasing Rim Homes stock is obtained by adding the
Thus, the expected payoff for the act of purchasing Rim Homes stock is $1,760.
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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 20 Solutions
Statistical Techniques in Business and Economics
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