SIEO 3600 (IEOR Majors)
Assignment #10
Introduction to Probability and Statistics
April 6, 2010
Assignment #10
– due April 13th, 2010
(
Central limit theorem, maximum likelihood estimator
)
1. Charity University announces a fund raising target of $10 millions.
It sends out
n
letters
to its alumni. From past experience, there is a probability of 0.6 that each alumni will not
respond at all.
Given that an alumni does respond (with probability 0.4), the amount of
contribution is a random variable with mean $
μ
and standard deviation $
σ
.
(a) What is the mean and variance of the amount of contribution from each letter sent?
(b) We can reasonably assume that each letter recipient will behave independently with the
above characteristic. What is the minimum number of letters to send so that Charity
University will hit its target with at least 90% probability?
Hint:
Think about the firehydrant example discussed in class.
2. A roulette wheel has 38 slots, numbered 0, 00, and 1 through 36. If you bet 1 on a specified
number, you either win 35 if the roulette ball lands on that number or lose 1 if it does not.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 YUNANLIU
 Normal Distribution, Probability theory, maximum likelihood estimator, Charity University

Click to edit the document details