| 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) |