# Syllabus

## Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

## Topics

### Maximum Likelihood Estimators

• Properties
• Fisher Information
• Asymptotic Variance of MLE

### Parameters of Normal Distribution

• Chi-squared and t-Distribution
• Distribution of the Estimates of Parameters of Normal Distribution
• Confidence Intervals

### Testing Hypotheses

• t-Tests and F-Tests
• Bayes Tests
• Most Powerful Tests (Including Randomized)

### Goodness-of-fit Tests

• Simple Discrete
• Continuous
• Composite Goodness-of-fit Tests
• Independence and Homogeneity Tests
• Kolmogorov-Smirnov Test

### Linear Regression

• Estimating Parameters
• Joint Distribution of Estimates
• Confidence and Prediction Intervals
• Joint Confidence Sets

### Multiple Regression, Analyses of Variance and Covariance

• Distribution of Estimates
• Testing General Linear Hypotheses

ACTIVITIES weightS
Ten Problem Sets 10 points each
Two Midterm Exams 150 points each

## Text

DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Boston, MA: Addison-Wesley, 2002.

## Calendar

The calendar below provides information on the course's lecture (L) and exam (E) sessions.

SES # TOPICS KEY DATES
L1 Overview of some Probability Distributions
L2 Maximum Likelihood Estimators
L3 Properties of Maximum Likelihood Estimators Problem set 1 due
L4 Multivariate Normal Distribution and CLT
L5 Confidence Intervals for Parameters of Normal Distribution Problem set 2 due
L6 Gamma, Chi-squared, Student T and Fisher F Distributions Problem set 3 due
L7-L8 Testing Hypotheses about Parameters of Normal Distribution, t-Tests and F-Tests Problem set 4 due in Ses #L8
L9

Testing Simple Hypotheses

Bayes Decision Rules

Problem set 5 due
E1 Exam 1
L10 Most Powerful Test for Two Simple Hypotheses
L11 Chi-squared Goodness-of-fit Test
L12 Chi-squared Goodness-of-fit Test for Composite Hypotheses
L13 Tests of Independence and Homogeneity Problem set 6 due
L14 Kolmogorov-Smirnov Test
L15-L16 Simple Linear Regression Problem set 7 due
L17-L18 Multiple Linear Regression Problem set 8 due
L19-L20

General Linear Constraints in Multiple Linear Regression

Analysis of Variance and Covariance

Problem set 9 due

Problem set 10 due in Ses #L20

E2 Exam 2