### Syllabus

### Homework

### Sample Tests

- Sample Test 1
- Sample Test 1
- Sample Test 2
- Sample Test 2
- Sample Final
- Sample Final
### Solution to Homework Assignments

- Homework 1
- Homework 2
- Homework 3
- Homework 4
- Homework 5
- Homework 6
- Homework 7
- Homework 8
- Homework 9
- Homework 10
- Homework 11
### Solution to Tests

- Test 1
- Test 2
### Class Diary

**Monday, 08/28:**Basic principle of counting (multiplication rule), permutations.**Read:**Sections 1.2 and 1.3.**Wedensday, 08/30:**combinations, number of integer solutions of equations**Read:**Sections 1.4 and 1.6.**Friday, 09/01:**binomial theorem, multinormial theorem, sample space, events.**Read:**Sections 1.5 and 2.2.**Wedensday, 09/06:**axioms of probability, simple properties of probability measures, sample spaces having equally likely outcomes.**Read:**Sections 2.3, 2.4 and 2.5.**Friday, 09/08:**sample spaces having equally likely outcomes.**Read:**Section 2.5.**Monday, 09/11:**sample spaces having equally likely outcomes, conditional probability.**Read:**Sections 2.5 and 3.2**Wedensday, 09/13:**Conditional probability, Bayes rule**Read:**Sections 3.2 and 3.3**Friday, 09/15:**Bayes rule, independent events.**Read:**Sections 3.3 and 3.4.**Monday, 09/18:**Independent events, independent trails, problem of points.**Read:**Section 3.4.**Wedensday, 09/20:**gambler's ruin, random variables.**Read:**Sections 3.4 and 4.1**Friday, 09/22:**discrete random variables, properties of distribution functions**Read:**Sections 4.2, 4.10 and 4.3**Monday, 09/25:**expectation of a function of a discrete random variable, moments, variance.**Read:**Sections 4.4 and 4.5.**Wedensday, 09/27:**Bernoulli random variables, binomial random variables.**Read:**Section 4.6.**Friday, 09/29:**Poisson random variables.**Read:**Sections 4.6 and 4.7**Monday, 10/02:**Poisson random variables, geometric random variables, negative binomial random variables**Read:**Sections 4.7 and 4.8**Wedensday, 10/04:**negative binomial random variables, expectation of sum of random variables**Read:**Sections 4.8 and 4.9**Friday, 10/06:**Continuous random variables, densities, absolutely continuous random variables, expectations of absolutely continuous random variables**Read:**Sections 5.1 and 5.2**Monday, 10/09:**Eexpectation of a function of an absolutely continuous random variable, variance of an absolutely continuous random variable, uniform random variables**Read:**Sections 5.2 and 5.3.**Wedensday, 10/11:**review, normal random variables**Read:**Section 5.4.**Friday, 10/13:**Test 1. Grades distribution: 100**2**, 95--99**10**, 90--94**12**, 85--89**8**, 80--84**2**, 75--79**10**, 70--74**2**, 65--69**1**, 60--64**1**, 50--59**1**, 40--49**1**.**Median**87.**Monday, 10/16:**DeMoivre-Laplace central limit theorem, application to polling.**Read:**Section 5.4.**Wedensday, 10/18:**Exponential random variables and gamma random variables.**Read:**Sections 5.5 and 5.6.**Friday, 10/20:**Gamma random variables, the distribution of a function of a random variable.**Read:**Sections 5.6 and 5.7**Monday, 10/23:**Joint distributions, marginal distributions, joint mass functions, marginal mass functions, joint densities, marginal densities.**Read:**Section 6.1**Wedensday, 10/25:**Joint distribution of n random variables, joint mass function of n random vaiables, joint density of n random variables, multinomial distribution, independent random variables.**Read:**Sections 6.1 and 6.2**Friday, 10/27:**Independent random variables.**Read:**Section 6.2**Moday, 10/30:**Sums of independent random variables.**Read:**Section 6.3**Wedensday, 11/01:**Sums of independent random variables; Conditional distributions: discrete case.**Read:**Sections 6.3 and 6.4**Friday, 11/03:**Conditional distributions.**Read:**Sections 6.4 and 6.5**Monday, 11/06:**Order statistics, expectation of a function of random variables.**Read:**Sections 6.6 and 7.2**Wedensday, 11/08:**Expectation of sums of random variables.**Read:**Section 7.2**Friday, 11/10:**Covariance, correlation coefficients, properties of covariances.**Read:**Section 7.4**Monday, 11/13:**Variance of sums**Read:**Section 7.4**Wedensday, 11/15:**Review for Test 2**Friday, 11/17:**Test 2: Grades distribution: 100**1**, 95--99**2**, 90--94**1**, 85--89**3**, 80--84**6**, 75--79**6**, 70--74**3**, 65--69**2**, 60--64**4**, 55--59**5**, 50--54**5**, 45--49**1**, 40--44**3**, 35--39**1**, 30--34**1**, 20--29**1**, --19**1**.**Median**68.**Monday, 11/27:**Conditional expectation**Read:**Section 7.5**Wedensday, 11/29:**Conditional expectation, moment generating functions**Read:**Sections 7.5 and 7.7**Friday, 12/01:**Moment generating functions, Markov inequality**Read:**Sections 7.7 and 8.2**Monday, 12/04:**Chebyshev inequality, weak law of large numbers, strong law numbers**Read:**Sections 8.2 and 8.4**Wedensday, 12/06:**Central limit theorem**Read:**Section 8.3**Friday, 12/08:**Review**Read:****Monday, 12/11:****Read:****Wedensday, 12/13:**