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, CauchySchwartz 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  Chisquare Distribution, tdistribution, 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  ttest  
32  Twosample ttest, Goodnessoffit Tests, Pearson's Theorem  
33  Simple Goodnessoffit Test, Composite Hypotheses  
34  Contingency Tables, Tests of Independence and Homogeneity  Problem set 8 due 
35  KolmogorovSmirnov Goodnessoffit Test  
36  Review of Test 2  
37  Review for the Final Exam  
Final Exam 