Midterm Examination # 1
Sta 113: Probability and Statistics in Engineering Tuesday, 2008 Sep. 23, 1:15 2:30 pm
This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the oor). You may use a single sheet
Jointly distributed random variables
Joint distributions and the central limit theorem
Artin Armagan
Sta. 113 Chapter 5 of Devore
February 5, 2009
Artin Armagan
Joint distributions and the central limit theorem
Jointly distributed random variables
Table o
General concepts Properties of estimators Maximum Likelihood estimation Bayesian inference
Point estimation
Artin Armagan
Sta. 113 Chapter 6 of Devore
February 12, 2009
Artin Armagan
Point estimation
General concepts Properties of estimators Maximum Likel
Normal distribution known variance Large sample CI, or CLT to the rescue Small sample normal, thank Guinness Condence intervals on the spread or variance Condence bounds Sample size computations
Condence intervals
Artin Armagan
Sta. 113 Chapter 7 of Devor
Hypotheses and test procedures Tests for population means P-values
Hypothesis testing
Artin Armagan
Sta 113 Chapter 8 Devore
November 2, 2009
Artin Armagan
Hypothesis testing
Hypotheses and test procedures Tests for population means P-values
Table of cont
Two sample tests
Inferences Based on Two Samples
Artin Armagan
STA 113 Chapter 9 of Devore
November 5, 2009
Artin Armagan
Inferences Based on Two Samples
Two sample tests
Table of contents
1
Two sample tests Normal known variance Large sample tests Normal
Simple Linear Regression Multiple Linear Regression
Simple and Multiple Linear Regression
Artin Armagan
Sta. 113 Chapter 12 and 13 of Devore
March 31, 2009
Artin Armagan
Simple and Multiple Linear Regression
Simple Linear Regression Multiple Linear Regres
Simple Linear Regression Analysis Multiple Linear Regression
STA113: Probability and Statistics in Engineering
Linear Regression Analysis - Chapters 12 and 13 in Devore
Artin Armagan
Department of Statistical Science
November 18, 2009
Armagan
Simple Linea
Is The Relationship Really Linear? How About Residuals? Inuential Observations Example
STA113
Regression Diagnostics
Artin Armagan
Department of Statistical Science
November 18, 2009
Armagan
Is The Relationship Really Linear? How About Residuals? Inuentia
Examples on Maximum Likelihood Estimation and Bayesian Inference
November 13, 2009
1
1.1
Estimating a Normal Population Mean
Unknown , Known 2
Let Xi N (, 2 ) where 2 is known and is to be estimated based on the observed n samples, x1 , ., xn . To be able
7.1
a. z/2 = 2.81 suggests that /2 = 1 (2.81) = 0.0025. Thus = 0.005 and the corresponding condence level is 99.5%. b. z/2 = 1.44 suggests that /2 = 1 (2.81) = 0.075. Thus = 0.15 and the corresponding condence level is 85%. c. 99.7% implies an value of 0.
STA113 - Probability and Statistics in Engineering, Fall09 Instructors: Sayan Mukherjee and Artin Armagan e-mail: sayan@stat.duke.edu, artin@stat.duke.edu Oce: Old Chem 112, Old Chem 217 Oce hours: TBA Textbook: Jay L. Devore, Probability and Statistics f
Midterm Examination # 3
Sta 113: Probability and Statistics in Engineering Thursday, 2006 Nov. 30, 1:15 2:30 pm
This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the oor). You may use a single sheet
Continuous random variables Continuous distributions
Continuous random variables and probability distributions
Artin Armagan
Sta. 113 Chapter 4 of Devore
January 28, 2009
Artin Armagan
Continuous random variables and probability distributions
Continuous r
Random variables Distributions for discrete random variables Expectation and variance Discrete distributions
Discrete random variables and probability distributions
Artin Armagan
Sta. 113 Chapter 3 of Devore
January 16, 2009
Artin Armagan
Discrete random
Discrete probability
Introduction to discrete probability
Artin Armagan
STA 113 Chapter 2 of Devore
January 8, 2009
Artin Armagan
Introduction to discrete probability
Discrete probability
Table of contents
1
Discrete probability Set theory Axioms Properti
Midterm Examination # 1
Sta 113: Probability and Statistics in Engineering Thursday, 2007 Sep. 20, 1:15 2:30 pm
This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the oor). You may use a single sheet
Midterm Examination # 1
Sta 113: Probability and Statistics in Engineering Thursday, 2007 Sep. 20, 1:15 2:30 pm
This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the oor). You may use a single sheet
Midterm Examination # 2
Sta 113: Probability and Statistics in Engineering Tuesday, 2008 Oct. 30, 1:15 2:30 pm
This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the oor). You may use a single sheet
Midterm Examination # 2
Sta 113: Probability and Statistics in Engineering Thursday, 2007 Oct. 25, 1:15 2:30 pm
This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the oor). You may use a single sheet
Midterm Examination # 1
Sta 113: Probability and Statistics in Engineering Thursday, 2006 Oct. 26, 1:15 2:30 pm
This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the oor). You may use a single sheet
Practice Examination # 2
Sta 113: Probability and Statistics in Engineering October 25, 2006
This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the oor). You may use a single sheet of notes or formul
Bayesian Inference
STA 113 Artin Armagan
Tuesday, November 10, 2009
Bayes Rule.s!
Reverend Thomas Bayes
Posterior
Prior
p(|y) = p(y|)p()/p(y)
Likelihood - Sampling Distribution
Normalizing Constant: p(y|)p()d
Tuesday, November 10, 2009
Flipping the Coin
O
Using Normal Distribution Using Exponential Distribution
Examples 1
Artin Armagan
Sta. 113
February 3, 2009
Artin Armagan
Examples 1
Using Normal Distribution Using Exponential Distribution
Table of contents
1
Using Normal Distribution
2
Using Exponential
STAT113 HW3 Solutions 1. (Chapter 4: 100 ) Solution: (a) Two conditions are required for f (x) to be a legitimate pdf: i. f (x) > 0, x > 0. 0 1 ii. f (x)dx = 32/(x + 4)3 dx = 32 =1 2(x + 4)2 0 0 (b) Let F (x) denote the cdf of X.
x x
09/18/09
F (x) =
0
f
STAT113 HW3
For Quiz 09/18/09
1. (Chapter 4: 100 ) Let X denote the time to failure (in years) of a certain hydraulic component. Suppose the pdf of X is f (x) = 32/(x + 4)3 for x > 0. (a) (b) (c) (d) (e) Verify that f (x) is a legitimate pdf. Determine th