### 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
### Lecture Slides

- 08/24
- 08/26
- 08/28
- 08/31
- 09/02
- 09/04
- 09/09
- 09/11
- 09/14
- 09/16
- 09/18
- 09/21
### Solution to Tests

- Test 1
- Test 2
### Class Diary

**Monday, 08/24:**Basic principle of counting (multiplication rule), permutations, combinations.**Read:**Sections 1.2, 1.3 and 1.4**Wedensday, 08/26:**combinations, binomial theorem, multinomial coefficients, multinormial theorem, number of integer solutions of equations**Read:**Sections 1.4, 1.5 and 1.6.**Friday, 08/28:**sample space, events, axioms of probability, simple properties of probability measures**Read:**Sections 2.2, 2.3, 2.4**Monday, 08/31:**sample spaces having equally likely outcomes.**Read:**Section 2.5.**Wedensday, 09/02:**sample spaces having equally likely outcomes, conditional probability.**Read:**Sections 2.5 and 3.2**Friday, 09/04:**Conditional probability, Bayes rule**Read:**Sections 3.2 and 3.3**Wedensday, 09/09:**Independent events, independent trails.**Read:**Section 3.4**Friday, 09/11:**problem of points, gambler's ruin, random variables.**Read:**Sections 3.4 and 4.1**Monday, 09/14:**random variables, distribution functions, discrete randim variables,probability mass functions, properties of distribution functions**Read:**Section 41, 4.2, 4.10**Wedensday, 09/16:**Expectation, expectation of a function of a discrete random variable, moments, variance.**Read:**Sections 4.3, 4.4, 4.5**Friday, 09/18:**Bernoulli random variables, binomial random variables, Poisson random variables**Read:**Sections 4.6 and 4.7**Monday, 09/21:**Poisson random variables, geometric random vraibles**Read:**Sections 4.7 and 4.8.**Wedensday, 09/23:**negative binomial random variables, expectation of sum of random variables.**Read:**Sections 4.8 and 4.9**Friday, 09/25:****Read:**Sections**Monday, 09/28:****Read:**Sections**Wedensday, 10/30:****Read:**Sections 4.8 and 4.9**Friday, 10/02:**Continuous random variables, densities, absolutely continuous random variables, expectations of absolutely continuous random variables**Read:**Sections 5.1 and 5.2**Monday, 10/05:**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, 10/07:**review, normal random variables**Read:**Section 5.4.**Friday, 10/09:**Test 1.**Monday, 10/12:**DeMoivre-Laplace central limit theorem, application to polling.**Read:**Section 5.4.**Wedensday, 10/14:**Exponential random variables and gamma random variables.**Read:**Sections 5.5 and 5.6.**Friday, 10/16:**Gamma random variables, the distribution of a function of a random variable.**Read:**Sections 5.6 and 5.7**Monday, 10/19:**Joint distributions, marginal distributions, joint mass functions, marginal mass functions, joint densities, marginal densities.**Read:**Section 6.1**Wedensday, 10/21:**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, 10/23:**Independent random variables.**Read:**Section 6.2**Moday, 10/26:**Sums of independent random variables.**Read:**Section 6.3**Wedensday, 10/28:**Sums of independent random variables; Conditional distributions: discrete case.**Read:**Sections 6.3 and 6.4**Friday, 11/30:**Conditional distributions.**Read:**Sections 6.4 and 6.5**Monday, 11/02:**Order statistics, expectation of a function of random variables.**Read:**Sections 6.6 and 7.2**Wedensday, 11/04:**Expectation of sums of random variables.**Read:**Section 7.2**Friday, 11/06:**Covariance, correlation coefficients, properties of covariances.**Read:**Section 7.4**Monday, 11/09:**Variance of sums**Read:**Section 7.4**Wedensday, 11/11:****Friday, 11/13:**Test 2**Monday, 11/16:**Conditional expectation**Read:**Section 7.5**Wedensday, 11/18:**Conditional expectation, moment generating functions**Read:**Sections 7.5 and 7.7**Friday, 11/20:**Moment generating functions, Markov inequality**Read:**Sections 7.7 and 8.2**Monday, 12/02:**Chebyshev inequality, weak law of large numbers, strong law numbers**Read:**Sections 8.2 and 8.4**Wedensday, 12/04:**Central limit theorem**Read:**Section 8.3**Friday, 12/06:**Review**Read:****Monday, 12/09:****Read:****Wedensday, 12/11:**