 ## 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

• 08/23
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
11/08
11/10
11/15
11/17
11/19
11/29
12/01
12/03
12/06
12/08

• 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
• Monday, 08/30: sample spaces having equally likely outcomes.
• Wedensday, 09/01: sample spaces having equally likely outcomes, conditional probability.
• Friday, 09/03: Conditional probability, Bayes rule
• Wedensday, 09/08: Independent events, independent trails.
• Friday, 09/10: problem of points, gambler's ruin, random variables.
• Monday, 09/13: random variables, distribution functions, discrete randim variables,probability mass functions, properties of distribution functions
• Wedensday, 09/15: Expectation, expectation of a function of a discrete random variable, moments, variance.
• Friday, 09/17: Bernoulli random variables, binomial random variables, Poisson random variables
• Monday, 09/20: Poisson random variables, geometric random vraibles
• Wedensday, 09/22: negative binomial random variables, expectation of sum of random variables.
• Friday, 09/24: expectation of sum of random variables, Continuous random variables, densities, absolutely continuous random variables.
• Monday, 09/27: absolutely continuous random variables, expectations of absolutely continuous random variables, Eexpectation of a function of an absolutely continuous random variable.
• 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
• Monday, 10/04: DeMoivre-Laplace central limit theorem, application to polling.
• Wedensday, 10/06: review,
• Friday, 10/08: Test 1. 100: 1, 90-99: 1, 85-89: 2, 80-84: 2, 75-79: 3, 70-74: 1, 60-69: 2, -59: 2
• Monday, 10/11: Exponential random variables, memoryless property, Gamma function
• Wedensday, 10/13: Gamma random variables, Beta random variables, the distribution of a function of a random variable
• 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
• 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.
• Wedensday, 10/20: independent random variables, Sums of independent random variables.
• Friday, 10/22: Sums of independent random variables.
• Monday, 10/25: Conditional distributions.
• Wedensday, 10/27: Order statistics, expectation of a function of random variables.
• Friday, 10/29: Covariance, correlation coefficients, properties of covariances.
• Monday, 11/01: Variance of sums
• Wedensday, 11/03: Conditional expectation
• Friday, 11/05: Conditional expectation, moment generating functions
• Monday, 11/07: moment generating functions
• Wedensday, 11/10: Review
• Friday, 11/12: Test 2. 90-99: 2, 80-84: 2, 70-75: 1, 65-69: 2, 60-64: 1, 55-59: 1, 50-54: 1, 40-49: 2, -39: 1
• Monday, 11/15: Markov inequality, Chebyshev inequality, weak law of large numbers