### 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

- 08/23
- 08/25
- 08/27
- 08/30
- 09/01
- 09/03
- 09/08
- 09/10
- 09/13
- 09/15
- 09/17
- 09/20
- 09/22
- 09/24
- 09/27
- 09/29
- 10/01
- 10/04
- 10/06
- 10/11
- 10/13
- 10/15
- 10/18
- 10/20
- 10/22
- 10/25
- 10/27
- 10/29
- 11/01
- 11/03
- 11/05
- 11/07
- 11/10
- 11/15
- 11/17
- 11/19
- 11/29
- 12/01
- 12/03
### Solution to Tests

- Test 1
- Test 2
### Class Diary

**Monday, 08/23:**Basic principle of counting (multiplication rule), permutations, combinations.**Read:**Sections 1.2, 1.3 and 1.4**Wedensday, 08/25:**combinations, binomial theorem, multinomial coefficients, multinormial theorem, number of integer solutions of equations**Read:**Sections 1.4, 1.5 and 1.6.**Friday, 08/27:**sample space, events, axioms of probability, simple properties of probability measures**Read:**Sections 2.2, 2.3, 2.4**Monday, 08/30:**sample spaces having equally likely outcomes.**Read:**Section 2.5.**Wedensday, 09/01:**sample spaces having equally likely outcomes, conditional probability.**Read:**Sections 2.5 and 3.2**Friday, 09/03:**Conditional probability, Bayes rule**Read:**Sections 3.2 and 3.3**Wedensday, 09/08:**Independent events, independent trails.**Read:**Section 3.4**Friday, 09/10:**problem of points, gambler's ruin, random variables.**Read:**Sections 3.4 and 4.1**Monday, 09/13:**random variables, distribution functions, discrete randim variables,probability mass functions, properties of distribution functions**Read:**Section 4.1, 4.2, 4.10**Wedensday, 09/15:**Expectation, expectation of a function of a discrete random variable, moments, variance.**Read:**Sections 4.3, 4.4, 4.5**Friday, 09/17:**Bernoulli random variables, binomial random variables, Poisson random variables**Read:**Sections 4.6 and 4.7**Monday, 09/20:**Poisson random variables, geometric random vraibles**Read:**Sections 4.7 and 4.8.**Wedensday, 09/22:**negative binomial random variables, expectation of sum of random variables.**Read:**Sections 4.8 and 4.9**Friday, 09/24:**expectation of sum of random variables, Continuous random variables, densities, absolutely continuous random variables.**Read:**Sections 4.9 and 5.1**Monday, 09/27:**absolutely continuous random variables, expectations of absolutely continuous random variables, Eexpectation of a function of an absolutely continuous random variable.**Read:**Sections 5.1 and 5.2**Wedensday, 09/29:**variance of an absolutely continuous random variable, uniform random variables, standard normal density**Read:**Sections 5.2, 5.3 and 5.4**Friday, 10/01:**normal random variables**Read:**Section 5.4**Monday, 10/04:**DeMoivre-Laplace central limit theorem, application to polling.**Read:**Section 5.4**Wedensday, 10/06:**review,**Read:****Friday, 10/08:**Test 1. 95-99:**2**, 90-94:**1**, 85-89:**2**, 80-84:**2**, 75-79:**3**, 70-74:**0**, 60-69:**2**, -59:**2****Monday, 10/11:**Exponential random variables, memoryless property, Gamma function**Read:**Sections 5.5 and 5.6**Wedensday, 10/13:**Gamma random variables, Beta random variables, the distribution of a function of a random variable**Read:**Sections 5.6 and 5.7**Friday, 10/15:**distribution of a function of a random variable, joint distributions, marginal distributions, joint mass functions, marginal mass functions, joint densities, marginal densities**Read:**Sections 5.7 and 6.1**Monday, 10/18:**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**Wedensday, 10/20:**independent random variables, Sums of independent random variables.**Read:**Sections 6.2 and 6.3**Friday, 10/22:**Sums of independent random variables.**Read:**Section 6.3**Monday, 10/25:**Conditional distributions.**Read:**Sections 6.4 and 6.5**Wedensday, 10/27:**Order statistics, expectation of a function of random variables.**Read:**Sections 6.6 and 7.2**Friday, 10/29:**Covariance, correlation coefficients, properties of covariances.**Read:**Section 7.4**Monday, 11/01:**Variance of sums**Read:**Section 7.4**Wedensday, 11/03:**Conditional expectation**Read:**Section 7.5**Friday, 11/05:**Conditional expectation, moment generating functions**Read:**Sections 7.5 and 7.7**Monday, 11/08:**moment generating functions**Read:**Section 7.7**Wedensday, 11/10:**Review**Friday, 11/12:**Test 2**Monday, 11/15:**Markov inequality, Chebyshev inequality, weak law of large numbers**Read:**Section 8.2**Wedensday, 11/17:**Central limit theorem**Read:**Section 8.3**Friday, 11/19:**strong law numbers**Read:**Section 8.4**Monday, 11/29:**Review,**Read:****Wedensday, 12/01:**Review**Friday, 12/03:**Review**Monday, 12/06:**Review**Wedensday, 12/08:**