18.650 (formerly 18.443) | Fall 2006 | Undergraduate

Statistics for Applications


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


Probability and Random Variables (18.440) or Probabilistic Systems Analysis (6.041)


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


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


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


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

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

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

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  

Course Info

As Taught In
Fall 2006
Learning Resource Types
Lecture Notes
Problem Sets