Parameter Estimation
An unknown parameter denoted by random variable Initially we have a prior p (This is a Bayesian framework) After making an observation X, we have a model px| We want to estimate What about the classical case (non- Bayesian)?
IE 300/G

IE 300 / GE 331 Spring 2009 Homework #1
Due: Feb. 5th
Problem 1. Let A and B be two sets. (a) Show that Ac = (Ac B) (Ac Bc ), (b) Show that (A B)c = (Ac B) (Ac Bc ) (A Bc ). (c) Consider rolling a fair six-sided die. Let A be the set of outcomes where the

IE 300 / GE 331 Spring 2009 Homework #6
Problem 1. Professor May B. Hard, who has a tendency to give difficult problems in probability quizzes, is concerned about one of the problems she has prepared for an upcoming quiz. She therefore asks her TA to solv

Discussion 1 of Week 2, Jan 26 1. A trucking firm has a contract to ship a load of goods from city W to city Z. There are no direct routes connecting W to Z, but there are 6 roads from W to X and 5 roads from X to Z. How many total routes are there to be

Inference for two samples
Chapter 10
Not covered: 10-5
1
Comparing two populations
Does a diet and exercise program reduce blood cholesterol level?
Compare means of blood cholesterol level before/after
Does Aspirin reduce heart attack risk?
Compare hear

IE 300 / GE 331 Discussion Problem Set 3
3-76
Let X denote the number of patients with heart failures due to outside factors. Then it has a binomial distribution with n= 20 and p= 0.13. Note that the pmf for a binomial random variable is as follows: P(X=

IE 300 / GE 331 Discussion Problem Set 4 4-5 (a), (e), (f) a) The distribution of X is symmetric around 0. Therefore, P (0 < X ) = 0.5. e) ( < 0 > 0.5) = (1 <
1 x
f) P( x < X ) = 1.5 x 2dx = 0.5 x 3 = 0.5 0.5 x 3 = 0.05, x = 0.9655.
x
1
< 1) = 1.
4-6 (a),

IE 300 / GE 331 Discussion Problem Set 6
4-88 Let X denote the distance between two consecutive major cracks. X is exponential with 0.2 cracks/mile. a) P( X 10) e10 e2 0.1353 b) Let Y denote the number of cracks in 10 miles. Y has a Poisson distribution

IE 300 / GE 331 Discussion Problem Set 7
5-40
The graph of the range of
,
is 1 1 1 2 1 . 2.614 2.649 2 19 8.776 1.852. The correlation coefficient between , and is: 10 2 2 1 1 2/19
Covariance between 2 19
and
is 2 19
,
2 19
2 19
2 19
Now,
,
8.776
2.614 2.

IE 300 / GE 331 Discussion Problem Set 2
(Independence) 2-110 (a) Let A denote the event that a player defeats all four opponents in a game. Since the results from opponents are independent, we have (b) Let B denote the event that a player defeats at leas

IE 300 / GE 331 Discussion Problem Set 1
2-17 (Sample space and events) Describe both the sample space and the event at most four calls are needed to get connected
c = connected, b = busy, S = cfw_c, bc, bbc, bbbc, bbbbc, , E=cfw_c, bc, bbc, bbbc
2-19 (e

Descriptive statistics
Chapter 6
1
Statistics
Descriptive statistics organizing, summarizing and displaying data Inferential statistics using sample data to draw conclusions about a population Probability vs statistics:
Probability: population sample (d

Joint probability distributions
Chap 5, excluding 5-1.6
1
Two or more r.v.s
Often interested in more than one r.v.
Stock prices of eBay and Amazon GPA and salary
Joint probability distribution for multiple r.v.s Relation between r.v.s: correlation
2
Tw

Continuous random variables Chapter 4
excluding 4-9,4-10
1
Discrete random variables
Bernoulli, Binomial, Geometric, Poisson
Binomial: # of successes out of n trials Geometric: # of trials needed until first success Poisson: # of events occur in an interv

Discrete random variables Chapter 3
excluding 3-7.2, 3-8
1
Random variable
A quantity whose value depends on the outcome of a random experiment Airlines sell more tickets than the plane can hold:
chance that every passenger who shows up can take the fli

GE 331 Analytic methods for uncertainty IE 300 Analysis of data
Liming Feng
1
Course objectives
Introductory probability and statistics: analyze data, make decisions Objectives
Learn basic probability/statistics concepts & techniques Learn how to conduc

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IE 300 / GE 331 HW1
2-44 (3 points)
a. Every arrangement of 7 locations selected from the 12 leads to a different design. 12! P712 = = 399,1680 designs are possible. 5! 12 12! b. Every subset of 7 locations selected from the 12 le

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IE 300 / GE 331 HW2
2-122 (4 points) (a) Let D denote the event that an item selected for inspection is classified as defective; let G denote the event that an item is good (i.e., non-defective). (b) ( | ) = ( ) = (| )( ) + (| )(

ADNumber_ Name_ Score_ IE300/GE331HW3
(2.5 points) The cumulative distribution function of a random variable X is given in 4-22. Determine the probability density function of X
(2.5 points) Compute the mean of X
(2.5 points) What is the standard deviation

Confidence Intervals
Chapter 8, all sections except 8-7
1
Estimate population mean
Estimate population mean using sample mean Accuracy/precision: sampling distribution (CLT or normal population)
X ~ N ( , 2 / n)
Measure of precision: standard error
SE :

Parameter Estimation
Chapter 7 (7-4.1,7-4.3 excluded)
Inferential statistics
Using sample data to draw conclusions about a population Inferential statistics
Parameter estimation (mean, variance, proportion) Confidence interval Testing hypotheses (statem

HW2: Page 2 of this document Print out page 2 and work on it directly. It will be accepted in this way only. All others will be returned without grading. If you need extra space, use the back of the page and note that you have done so. Please write down y

HW1: Page 2 of this document Print out page 2 and work on it directly. It will be accepted in this way only. All others will be returned without grading. If you need extra space, use the back of the page and note that you have done so. Please write down y

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IE 300 / GE 331 HW7
From http:/finance.yahoo.com, download daily prices for NASDAQ-100 (^NDX) and Google Inc. (Goog) from 8/19/2004 to 03/26/2010. Create a csv file containing 5 columns: one column for the date, two columns for the

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IE 300 / GE 331 HW6
Amazon_Monthly.txt contains monthly prices and returns of Amazon's stock. Use R to compute the following. Copy and paste your R commands and outputs to this word file, and identify the required quantities. Solut