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