| ACTIVITIES | weightS |
|---|---|
| Ten Problem Sets | 10 points each |
| Two Midterm Exams | 150 points each |
Table of Contents
Syllabus
Syllabus
 When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more. |
Prerequisites
Probability and Random Variables (18.440) or Probabilistic Systems Analysis (6.041)
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
- Testing Hypotheses about Parameters
- Confidence and Prediction Intervals
- Joint Confidence Sets
Multiple Regression, Analyses of Variance and Covariance
- Distribution of Estimates
- Testing General Linear Hypotheses
Grading
Text
DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Boston, MA: Addison-Wesley, 2002. ISBN: 0201524880.
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 | |
| L21 | Classification Problem, AdaBoost Algorithm | |
| L22 | Review |