 ## 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

• 08/24
08/26
08/28
08/31
09/02
09/04
09/09
09/11
09/14
09/16
09/18
09/21
09/23
09/25
09/28
09/30
10/02
10/05
10/07
10/12
10/14
10/16
10/19
10/21
10/23
10/26
10/28
10/30
11/02
11/04
11/06
11/09
11/11
11/16
11/18
11/20
11/30

• 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
• Monday, 08/31: sample spaces having equally likely outcomes.
• Wedensday, 09/02: sample spaces having equally likely outcomes, conditional probability.
• Friday, 09/04: Conditional probability, Bayes rule
• Wedensday, 09/09: Independent events, independent trails.
• Friday, 09/11: problem of points, gambler's ruin, random variables.
• Monday, 09/14: random variables, distribution functions, discrete randim variables,probability mass functions, properties of distribution functions
• Wedensday, 09/16: Expectation, expectation of a function of a discrete random variable, moments, variance.
• Friday, 09/18: Bernoulli random variables, binomial random variables, Poisson random variables
• Monday, 09/21: Poisson random variables, geometric random vraibles
• Wedensday, 09/23: negative binomial random variables, expectation of sum of random variables.
• Friday, 09/25: expectation of sum of random variables, Continuous random variables, densities, absolutely continuous random variables.
• Monday, 09/28: absolutely continuous random variables, expectations of absolutely continuous random variables, Eexpectation of a function of an absolutely continuous random variable.
• Wedensday, 10/30: variance of an absolutely continuous random variable, uniform random variables, standard normal density
Read: Sections 5.2, 5.3 and 5.4
• Friday, 10/02: normal random variables
• Monday, 10/05: DeMoivre-Laplace central limit theorem, application to polling.
• Wedensday, 10/07: review,
• Friday, 10/09: Test 1.
• Monday, 10/12: Exponential random variables, memoryless property, Gamma function
• Wedensday, 10/14: Gamma random variables, Bdeta random variables, the distribution of a function of a random variable
• Friday, 10/16: distribution of a function of a random variable, joint distributions, marginal distributions, joint mass functions, marginal mass functions, joint densities, marginal densities
• Monday, 10/19: Joint distribution of n random variables, joint mass function of n random vaiables, joint density of n random variables, multinomial distribution, independent random variables.
• Wedensday, 10/21: independent random variables, Sums of independent random variables.
• Friday, 10/23: Sums of independent random variables.
• Monday, 10/26: Conditional distributions.
• Wedensday, 10/28: Order statistics, expectation of a function of random variables.
• Friday, 10/30: Covariance, correlation coefficients, properties of covariances.
• Monday, 11/02: Variance of sums
• Wedensday, 11/04: Conditional expectation
• Friday, 11/06: Conditional expectation, moment generating functions
• Monday, 11/09: moment generating functions
• Wedensday, 11/11: Review
• Friday, 11/13: Test 2
• Monday, 11/16: Markov inequality, Chebyshev inequality, weak law of large numbers