| 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) |