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Syllabus
Textbook
DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Pearson Addison
Wesley. ISBN: 0201524880.
Prerequisites
Probability and Random Variables (18.440) or Probabilistic Systems Analysis (6.041).
Course Outline
We will cover parts of Chapters 6-10 (estimation, sampling distributions of estimators, testing
hypotheses, categorical data and non-parametric methods, and linear statistical models).
Necessary facts from probability will be recalled throughout the course. Some lectures will not
be limited to the textbook, so attendance is important.
Course Description
This course provides a broad treatment of statistics, concentrating on specific statistical
techniques used in science and industry.
Topics
Estimation Theory


Estimates by method of moments, their properties;
Maximum likelihood estimates, their properties, Fisher information, Rao-Cramer
inequality, efficient estimates;


Bayes estimates, prior and posterior distributions, conjugate priors;
Sufficient and jointly sufficient statistics, Neyman-Fisher factorization criterion, RaoBlackwell theorem;


Estimates for parameters of normal distribution, their properties;
Chi-square, Fisher and Student distributions, confidence intervals for parameters of
normal distribution.
Hypotheses Testing

Testing simple hypotheses, Bayes decision rules, types of error, most powerful tests,
likelihood ratio tests, randomized tests;

Composite hypotheses, power function, monotone likelihood ratio and uniformly most
powerful tests;


t-tests and F-tests;
Goodness-of-fit tests, chi-square tests, tests of independence and homogeneity,
Kolmogorov-Smirnov test.
Regression and Classification

Simple linear regression, least-squares fit, statistical inference in simple linear
regression, confidence intervals, prediction intervals;

Classification problem, boosting algorithm.
Grades
ACTIVITIES
POINTS
Homework
200 points
Two Midterm Tests
100 points each
Final Exam
200 points
Assignments
The assignments are handed out in the lecture sessions noted in the table and are due one
week later. The pages referred to in some of the problem sets are from the text: DeGroot,
Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Pearson Addison Wesley.
ISBN: 0201524880.
LEC #
ASSIGNMENTS
2
Problem Set 1 (PDF)
4
Problem Set 2 (PDF)
7
Problem Set 3 (PDF)
10
Problem Set 4 (PDF)
13
Problem Set 5 (PDF)
19
Problem Set 6 (PDF)
22
Problem Set 7 (PDF)
27
Problem Set 8 (PDF)
31
Problem Set 9 (PDF)
Calendar
The Problem sets are due one week after they are handed out.
LEC #
1
TOPICS
Estimation Theory
KEY
DATES
Introduction
2
Some Probability
Distributions
3
Method of Moments
4
Maximum Likelihood
Estimators
Problem
set 1 out
Problem
set 2 out
Consistency of MLE
5
Asymptotic Normality of
MLE, Fisher Information
6
Rao-Crámer Inequality
7
Efficient Estimators
8
Problem
set 3 out
Gamma Distribution
Beta Distribution
9
Prior and Posterior
Distributions
Bayes Estimators
10
11
Conjugate Prior
Distributions
Problem
set 4 out
Sufficient Statistic
Jointly Sufficient
Statistics
12
13
Improving Estimators
Using Sufficient
Statistics, Rao-Blackwell
Theorem
Minimal Jointly Sufficient
Statistics
χ2 Distribution
14
Estimates of Parameters
of Normal Distribution
15
Orthogonal
Transformation of
Standard Normal Sample
16
Fisher and Student
Distributions
Problem
set 5 out
17
Confidence Intervals for
Parameters of Normal
Distribution
Testing Hypotheses
18
Testing Simple
Hypotheses
Bayes Decision Rules
19
Most Powerful Test for
Two Simple Hypotheses
Problem
set 6 out
Randomized Most
Powerful Test
20
21
Composite Hypotheses,
Uniformly Most Powerful
Test
Monotone Likelihood
Ratio
One Sided Hypotheses
22
One Sided Hypotheses
(cont.)
23
Pearson's Theorem
Problem
set 7 out
Goodness-of-Fit Test
24
Goodness-of-Fit Test for
Continuous Distribution
25
Goodness-of-Fit Test for
Composite Hypotheses
26
Test of Independence
27
Test of Homogeneity
28
Kolmogorov-Smirnov
Test
Simple Linear Regression
29
Method of Least Squares
Simple Linear Regression
30
Joint Distribution of the
Estimates
Problem
set 8 out
31
Statistical Inference in
Simple Linear Regression
32
Classification Problem
Problem
set 9 out