Schedule

Week Date Topic
   1 Th 09/22 Review of the course syllabus. Introduction and basic concepts. Sections 1.1-1.4. Kadane: 1.1
   2 Tu 09/27 Definition of probability and finite sample spaces. Sections 1.5-1.6. Kadane: 1.2,1.3.
    Th 09/29 Counting methods. Combinatorial methods. Multinomial coefficients. Sections 1.7-1.9.
   3   Tu 10/04 Union of events. Conditional probability and independent events. Sections 1.10 and 2.1-2.2. Kadane: 2.1, 2.2, 2.3
     Th 10/06 Bayes' Theorem. Section 2.3. Kadane: 2.4, 2.5, 2.6 
   4   Tu 10/11 Discrete random variables. Examples of discrete random variables. Sections 3.1, 5.1-5.5. 
    Th 10/13 Examples of discrete random variables. Continuous random variables. The CDF. Sections 5.1-5.5,  and 3.2-3.3. 
   5  Tu 10/18 Bivariate distributions and marginal distributions. Sections 3.4 and 3.5. 
     Th 10/20 Conditional distributions. Section 3.6
   6   Tu 10/25 Review
     Th 10/27 MIDTERM
   7   Tu 11/1 Multivariate distributions. Section 3.7. 
     Th 11/3 Functions of random variables. Sections 3.8-3.9.
   8   Tu 11/8 Markov chains. Section 3.10 
    Th 11/10 Expectation and variances. Section 4.1-4.3 and 5.1-5.5.  
   9   Tu 11/15 Moment generating functions. Covariance and conditional expectation. Sections 4.4-4.6. 
     Th 11/17 The normal distribution. Markov and Chebyshev's inequalities. The law of large numbers. Sections 5.6, 6.1-6.2.
   10   Tu 11/22 The law of large numbers and the central limit theorem. Sections 6.2-6.3
    Th 11/24 THANKSGIVING
   11  Tu 11/29 More CLT examples. Other distributions: the gamma and beta distributions. The Poisson process. 
   Th 12/01 Review. 
  Mo 12/05 FINAL EXAM (two hours: 1 - 3 PM)