## Math 461 Probability Theory

• ### Sample Tests

• Sample Test 1
Sample Test 1
Sample Test 2
Sample Test 2
Sample Final
Sample Final

• Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8
Homework 9
Homework 10
Homework 11

• Test 1
Test 2
• ### Class Diary

• Monday, 08/26: Basic principle of counting (multiplication rule), permutations.
Read: Sections 1.2 and 1.3.
• Wedensday, 08/28: combinations, number of integer solutions of equations
Read: Sections 1.4 and 1.6.
• Friday, 08/30: binomial theorem, multinormial theorem, sample space, events.
Read: Sections 1.5 and 2.2.
• Wedensday, 09/04: axioms of probability, simple properties of probability measures, sample spaces having equally likely outcomes.
Read: Sections 2.3, 2.4 and 2.5.
• Friday, 09/06: sample spaces having equally likely outcomes.
• Monday, 09/09: sample spaces having equally likely outcomes, conditional probability.
Read: Sections 2.5 and 3.2
• Wedensday, 09/11: Conditional probability, Bayes rule
Read: Sections 3.2 and 3.3
• Friday, 09/13: Bayes rule, independent events.
Read: Sections 3.3 and 3.4.
• Monday, 09/16: Independent events, independent trails.
• Wedensday, 09/18:problem of points, gambler's ruin, random variables.
Read: Sections 3.4 and 4.1
• Friday, 09/20: discrete random variables, properties of distribution functions
Read: Sections 4.2, 4.10 and 4.3
• Monday, 09/23: expectation of a function of a discrete random variable, moments, variance.
Read: Sections 4.4 and 4.5.
• Wedensday, 09/25: Bernoulli random variables, binomial random variables.
• Friday, 09/27:Poisson random variables.
Read: Sections 4.6 and 4.7
• Monday, 09/30: Poisson random variables, geometric random variables, negative binomial random variables
Read: Sections 4.7 and 4.8
• Wedensday, 10/02:negative binomial random variables, expectation of sum of random variables
Read: Sections 4.8 and 4.9
• Friday, 10/04: Continuous random variables, densities, absolutely continuous random variables, expectations of absolutely continuous random variables
Read: Sections 5.1 and 5.2
• Monday, 10/07: 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, 10/09: review, normal random variables
• Friday, 10/11: Test 1. Grades distribution: 100 3 , 95--99 5 , 90--94 5 , 85--89 5 , 80--84 2 , 75--79 0 , 70--74 2 , 65--69 4 , 60--64 2 , --59 1 Median 89 .
• Monday, 10/14: DeMoivre-Laplace central limit theorem, application to polling.
• Wedensday, 10/16: Exponential random variables and gamma random variables.
Read: Sections 5.5 and 5.6.
• Friday, 10/18: Gamma random variables, the distribution of a function of a random variable.
Read: Sections 5.6 and 5.7
• Monday, 10/21: Joint distributions, marginal distributions, joint mass functions, marginal mass functions, joint densities, marginal densities.
• Wedensday, 10/23: 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, 10/25: Independent random variables.
• Moday, 10/28: Sums of independent random variables.
• Wedensday, 10/30: Sums of independent random variables; Conditional distributions: discrete case.
Read: Sections 6.3 and 6.4
• Friday, 11/01: Conditional distributions.
Read: Sections 6.4 and 6.5
• Monday, 11/04: Order statistics, expectation of a function of random variables.
Read: Sections 6.6 and 7.2
• Wedensday, 11/06: Expectation of sums of random variables.
• Friday, 11/08: Covariance, correlation coefficients, properties of covariances.
• Monday, 11/11: Variance of sums
• Wedensday, 11/13: Review for Test 2
• Friday, 11/15: Test 2: Grades distribution: 100 1 , 95--99 2, 90--94 2, 85--89 3, 80--84 1, 75--79 3, 70--74 0, 65--69 1, 60--64 5, 55--59 2, 50--54 1, --49 3 Median 70.
• Monday, 11/18: Conditional expectation