Math 461 Probability Theory

Renming Song, Fall 2011

• Syllabus
  

• Homework
  

• Sample Tests
  

Sample Test 1

Sample Test 1

Sample Test 2

Sample Test 2

Sample Final

Sample Final

• Solution to Homework Assignments
  

Set 1

Set 2

Set 3

Set 4

Set 5

Set 6

Set 7

Set 8

Set 9

Set 10

Set 11

Set 12

• Solution to Tests
  

Test 1

Test 2

• Class Diary

• Monday, 08/22: basic principle of counting, generalized basic principle of counting, permutaions
  Read: Sections 1.2 and 1.3.
• Wedensday, 08/24: combinations, number of integer solutions of equations
  Read: Sections 1.4 and 1.6.
• Friday, 08/26:binomial theorem, multinormial theorem, sample space, events.
  Read: Sections 1.5 and 2.2.
• Monday, 08/29:axioms of probability, simple properties of probability measures.
  Read: Sections 2.3 and 2.4.
• Wedensday, 08/31:sample spaces having equally likely outcomes.
  Read: Section 2.5.
• Friday, 09/02:sample spaces having equally likely outcomes (continued).
  Read: Section 2.5.
• Wedensday, 09/07: Conditional probability
  Read: Section 3.2.
• Friday, 09/09: Bayes's formula, independent events.
  Read: Sections 3.3 and 3.4.
• Monday, 09/12: independent events (continued)
  Read: Section 3.4.
• Wedensday, 09/14: problem of points, gambler's ruin, random variables
  Read: Sections 3.4 and 4.1.
• Friday, 09/16: discrete random variables, properties of distribution functions
  Read: Sections 4.2 and 4.10
• Monday, 09/26: summary of expectation and variance of discrete random variables, expectation of a function of a discrete random variables, binomial random variables. Poisson random variables.
  Read: Sections 4.3--4.7
• Wedensday, 09/28: Poisson random variables (continued), geometric random variables
  Read: Sections 4.7--4.8
• Friday, 09/30: geometric random variables, negative binominal random variables.
  Read: Section 4.8
• Monday, 10/03: expectations of sums of random variables, continuous random variables, densities, absolutely continuous random variables
  Read: Section 4.9, Section 5.1
• Wedensday, 10/05: Review
• Friday, 10/07: Test
• Monday, 10/10: density, absolutely continuous random variables.
  Read:Section 5.1
• Wedensday, 10/12: expectation and variance of absolutely continuous random variables, uniform random variables.
  Read:Sections 5.2 and 5.3
• Friday, 10/14: normal random variables, normal approximation to binomial random variables.
  Read:Section 5.4.
• Monday, 10/17: application of normal approximation to polling, exponential random variables.
  Read:Section 5.5.
• Wedensday, 10/19: Gamma random variables
  Read:Section 5.6
• Friday, 10/21: finding teh density of a function of an absoluetly continuous random variable. joint distribution, marginal distribution, joint mass function, marginal mass function
  Read:Sections 5.7 and 6.1.
• Monday, 10/24: joint density, marginal density, multinomail distributions.
  Read:Section 6.1.
• Wedensday, 10/26: Independent random variables
  Read:Section 6.2.
• Friday, 10/28: Sums of independent discrete random variables
  Read:Section 6.3.
• Monday, 10/31: Sums of independent absolutely continuoius random variables
  Read:Section 6.3.
• Wedensday, 11/02: Conditiona distributions: discrete case.
  Read:Section 6.4.
• Friday, 11/04: Conditiona distributions: absolutely continuous case. order statistics.
  Read:Section 6.5 and 6.6.
• Monday, 11/07: Expectation of sums of random variables.
  Read:Section 7.2.
• Wedensday, 11/09: Review
• Friday, 11/11: Test 2
• Monday, 11/14: Expectation of sums of random variables (cont.)
  Read:Section 7.2.
• Wedensday, 11/16: Covariance, correlations
  Read:Section 7.4.
• Friday, 11/18: variance of the sums.
  Read:Section 7.4.
• Monday, 11/28: Conditional expectations
  Read:Section 7.5.
• Wedensday, 11/30: Computing expectation by conditioning, momemnt generating functions
  Read:Sections 7.5 and 7.7.