# Syllabus

## Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

## Textbook

DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Pearson Addison Wesley.

## 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, Rao-Blackwell 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.

ACTIVITIES  POINTS
Homework 200 points
Two Midterm Tests 100 points each
Final Exam 200 points