Introductory Probability:
Statistics 116

• Practicalities

  • About the Textbook -with link
  • Logistics
    • Office Hours
    • Approximate Class Schedule
  • Prerequisites
  • Exams and Assignments
    • Classattendance
    • Study Guide for the first midterm
  • Examples of Exams from past years
  • Solutions to the first midterm
  • Study Guide for Midterm 2
  • The Final
  • Homeworks
    • Homework 1
    • Homework 2: due Wed. Oct. 7th, before class
    • Homework 3: due Wed. Oct. 14th, before class
    • Homework 4: due Wed. Oct. 21st, before class
    • Homework 5: due Monday Nov. 2nd , before class
    • Homework 6: due Monday Nov. 9th, before class
    • Homework 7: due Wednesday Nov. 18th, before class
    • Homework 8: due Wednesday Nov. 25th, before class
    • Homework 9-optional if you did all others: due Wednesday Dec. 2nd, before class
    • Some Puzzles to think about
• Lecture Summaries

  • Basic Concepts
    • Probability
    • Sample Space 09/24
      • Matlab Dice Example from lecture 09/24/98
      • Definition of Probability 9/25
      • Discrete Uniform Random Distribution
      • Computer Simulation
      • Problem Session,09/25/98: De Méré's Problem
      • Another Matlab Example for dice game
    • Set Facts, Venn Diagrams 9/28
    • Properties of Probabilities 9/28
      • Tree Diagrams
      • Determination of probabilities 9/29
    • Infinite Sample Spaces 9/29
  • Continuous random variables 9/30
    • Examples
    • Monte Carlo Procedures for computing areas 9/30
      • Buffon's Needle - 9/30
    • Densities 10/2
      • Examples with simulations 10/2
    • Cumulative Distribution Function 10/5
    • Examples with functions of Uniform Random Numbers 10/5
  • Combinatorics
    • Enumeration Rules
      • Birthday Problem 10/6
      • Approximating n! 10/7
      • A note on doing symbolic computations
      • More about k-subsets 10/9
      • The matching Problem 10/9
      • Multinomial Coefficients and applications 10/12
  • Conditional Probability
    • Definition and Properties 10/12
    • Conditional Probability IS a probability 10/12
    • Examples of using conditional probability 10/13
    • Monty Hall 10/14
    • Independence 10/14 and 10/16
      • Independence of more than two events 10/20
      • The Craps principle 10/16
      • Example of computation for craps 10/19
    • Joint Distributions 10/19, 10/20
      • Gambler's Ruin 10/21
      • Joint Probability Distribution for n variables 10/21
    • Conditionning with continuous random variables
      • Jointly Distributed random Variables 10/26
      • Continuous Random Variables 10/26
      • Marginal Distributions10/26
      • Examples10/26
    • Independent Random Variables 10/26
      • Independence for Continuous Random Variables 10/27
    • Conditional Distributions 10/27
      • Conditional Density 10/28
      • Bayes Billiard Balls 10/28
      • Beta Random Variable 10/28
    • Order Statistics 10/30
      • Example with a Uniform Random Variable
  • Special Distributions
    • Binomial Distribution 10/29
      • Odds Ratios and Mode 10/30
    • Hypergeometric Random Variable 11/3
    • Geometric 11/3
    • Negative Binomial 11/3
    • Poisson random variable 11/2
      • Motivation
      • Definition 11/2
      • Parameters of Distributions 11/3
    • Special Continuous Distributions 11/2
      • Change of Variables 11/3
      • Exponential Random Variable 11/4
    • Normal Random Variables 11/4
      • Standard Normal Random Variable
      • Normal Random Variable
      • How was the constant found?
  • Expectation and Variance 11/6
    • Discrete Random Variable 11/6
      • Properties of Expectation 11/6
      • Pascal's rationalisation of religion
    • Indicator variables and Bernouilli variables
      • Examples of computing expectations of sums 11/9
      • Conditional Expectation 11/9
    • Variance 11/10
      • Conditional Expectation
    • Expectations and Variances for Continuous Random Variables 11/16
      • Properties
      • Variance 11/17
  • Special Lecture:11/18: Persi Diaconis on ESP
  • Sums of Random Variables 11/23
    • Discrete CAse
      • Sum of Poisson independent 11/24
    • Sums of Continuous Random Variables
      • Gamma density
      • Sum of two independent Normal random variables 11/25
  • Limit Theorems
    • Chebychev's Inequality
    • Weak Law of Large Numbers
    • The Central Limit Theorem
      • Polar Method for Generating Normal Random Variables 12/2
      • Web sites for the central limit theorem
• Section Summaries

  • Sample Spaces with Equally Likely Outcomes 10/1/98
  • Inclusion Exclusion Principle and Binomial 10/8/98
  • Inclusion Exclusion continued and Combinatorics 10/15/98
  • Geometric and Hypergeometric Distributions 10/29
• References

  • Reading Material
  • Web references
    • Applets to try out
    • Historical Websites
    • A very useful glossary
    • Sites with Matlab tutorials
• Index
• About this document ...