This is an archived course. A more recent version may be available at ocw.mit.edu.

Calendar

LEC # TOPICS KEY DATES
1 Probability, Set Operations  
2 Properties of Probability

Finite Sample Spaces, Some Combinatorics		  
3 Multinomial Coefficients, Union of Events  
4 Matching Problem, Conditional Probability Problem set 1 due
5 Independence of Events  
6 Solutions to Problem Set 1  
7 Bayes' Formula Problem set 2 due
8 Random Variables and Distributions  
9 Cumulative Distribution Function  
10 Marginal Distributions Problem set 3 due
11 Conditional Distributions, Multivariate Distributions  
12 Functions of Random Variables, Convolution  
13 Functions of Random Variables: Sum, Product, Ratio, Maximum, Change of Variables Problem set 4 due
14 Linear Transformations of Random Vectors, Review of Problem Set 4  
15 Review for Exam 1  
  Exam 1  
16 Expectation, Chebyshev's Inequality  
17 Properties of Expectation, Variance, Standard Deviation  
18 Law of Large Numbers, Median  
19 Covariance and Correlation, Cauchy-Schwartz Inequality  
20 Poisson Distribution, Approximation of Binomial Distribution, Normal Distribution  
21 Normal Distribution, Central Limit Theorem Problem set 5 due
22 Central Limit Theorem, Gamma Distribution, Beta Distribution  
23 Estimation Theory, Bayes' Estimators  
24 Bayes' Estimators Problem set 6 due
25 Maximum Likelihood Estimators  
26 Chi-square Distribution, t-distribution, Confidence Intervals for Parameters of Normal Distribution  
27 Confidence Intervals for Parameters of Normal Distribution Problem set 7 due
28 Review for Exam 2  
  Exam 2  
29 Hypotheses Testing, Bayes' Decision Rules  
30 Most Powerful Test for Two Simple Hypotheses  
31 t-test  
32 Two-sample t-test, Goodness-of-fit Tests, Pearson's Theorem  
33 Simple Goodness-of-fit Test, Composite Hypotheses  
34 Contingency Tables, Tests of Independence and Homogeneity Problem set 8 due
35 Kolmogorov-Smirnov Goodness-of-fit Test  
36 Review of Test 2  
37 Review for the Final Exam  
  Final Exam