Math 461 Probability Theory
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
- 01/17
- 01/19
- 01/22
- 01/24
- 01/26
- 01/29
- 01/31
- 02/02
- 02/05
- 02/07
- 02/09
- 02/12
- 02/14
- 02/16
- 02/19
- 02/21
- 02/23
- 02/26
- 02/28
- 03/04
- 03/06
- 03/08
- 03/18
- 03/20
- 03/22
- 03/25
- 03/27
- 03/29
- 04/01
- 04/03
- 04/05
- 04/08
- 04/10
- 04/15
- 04/17
- 04/19
- 04/22
- 04/24
- 04/29
- 05/01
Solution to Tests
- Test 1
- Test 2
Class Diary
- Wedensday, 01/17:
Basic principle of counting (multiplication rule), permutations, combinations.
Read: Sections 1.2, 1.3 and 1.4
- Friday, 01/19: combinations, binomial theorem, multinomial coefficients, multinormial theorem, number of integer solutions of
equations
Read: Sections 1.4, 1.5 and 1.6.
- Monday, 01/22: sample space, events, axioms of probability, simple properties
of probability measures
Read: Sections 2.2, 2.3, 2.4
- Wedensday, 01/24: sample spaces having equally likely outcomes.
Read: Section 2.5.
- Friday, 01/26: sample spaces having equally likely outcomes, conditional probability.
Read: Sections 2.5 and 3.2
- Monday, 01/29: Conditional probability, Bayes rule
Read: Sections 3.2 and 3.3
- Wedensday, 01/31: Independent events, independent trails.
Read: Section 3.4
- Friday, 02/02: problem of points, gambler's ruin, random variables.
Read: Sections 3.4 and 4.1
- Monday, 02/05: random variables, distribution functions, discrete randim variables,probability mass functions, properties of distribution functions
Read: Section 4.1, 4.2, 4.10
- Wedensday, 02/07: Expectation, expectation of a function of a discrete random variable, moments, variance.
Read: Sections 4.3, 4.4, 4.5
- Friday, 02/09: Bernoulli random variables, binomial random variables, Poisson random variables
Read: Sections 4.6 and 4.7
- Monday, 02/12: Poisson random variables, geometric random vraibles
Read: Sections 4.7 and 4.8.
- Wedensday, 02/14: negative binomial random variables, expectation of sum of random variables.
Read: Sections 4.8 and 4.9
- Friday, 02/16: expectation of sum of random variables, Continuous random variables, densities,
absolutely continuous random variables.
Read: Sections 4.9 and 5.1
- Monday, 02/19: 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, 02/21: variance of an
absolutely continuous random variable, uniform random variables, standard normal density
Read: Sections 5.2, 5.3 and 5.4
- Friday, 02/23: normal random variables
Read: Section 5.4
- Monday, 02/26: DeMoivre-Laplace central limit theorem,
application to polling.
Read: Section 5.4
- Wedensday, 02/28: review,
Read:
- Friday, 03/01: Test 1. Median: 86. Score distribution: 100 (6), 95--99 (6), 90--94 (4), 85--89 (5), 80--84 (3); 75--79 (5), 70--74 (2), 65--69 (1), 60--64 (2), 50--59 (0), 40--49 (2), --39 (1)
- Monday, 03/04: Exponential random variables, memoryless property, Gamma function
Read: Sections 5.5 and 5.6
- Wedensday, 03/06: Gamma random variables, Beta random variables, the distribution of
a function of a random variable
Read: Sections 5.6 and 5.7
- Friday, 03/08: 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, 03/18: 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, 03/20: independent random variables, Sums of independent random variables.
Read: Sections 6.2 and 6.3
- Friday, 03/22: Sums of independent random variables.
Read: Section 6.3
- Monday, 03/25: Conditional distributions.
Read: Sections 6.4 and 6.5
- Wedensday, 03/27: Order statistics, expectation of a function of
random variables.
Read: Sections 6.6 and 7.2
- Friday, 03/29: Covariance, correlation coefficients,
properties of covariances.
Read: Section 7.4
- Monday, 04/01: Variance of sums
Read: Section 7.4
- Wedensday, 04/03: Conditional expectation
Read: Section 7.5
- Friday, 04/05: Conditional expectation, moment generating functions
Read: Sections 7.5 and 7.7
- Monday, 04/08: moment generating functions
Read: Section 7.7
- Wedensday, 04/10: Review
- Friday, 04/12: Test 2. Median: 72. Score distribution: 95--99 (6);
90--94 (2); 85--89 (2); 80--84 (5); 70-74 (7); 65--69 (3); 60--64 (1); 55--59 (2); 50--54 (2); 45--49 (1); 30--44 (3); --39 (4)
- Monday, 04/15: Markov inequality, Chebyshev inequality, weak law of large numbers
Read: Section 8.2
- Wedensday, 04/17: Central limit theorem
Read: Section 8.3
- Friday, 04/19: strong law of large numbers
Read: Section 8.4
- Monday, 04/22: Review,
Read:
- Wedensday, 04/24: Review
- Friday, 04/26: Review
- Monday, 04/29: Review
- Wedensday, 05/01: Review