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

Lecture Notes

The lecture notes were taken by Anna Vetter, a student in the class.

LEC # TOPICS LECTURE NOTES
1 Probability, Set Operations (PDF)
2 Properties of Probability

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