| 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 |