Probability & Statistics I -- Lecture Presentations & Handouts

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Chapter 2 - Probability
       Probability and Inference (2.2) (revised 07/01/07)
       Review of Set Notation (2.3) (revised 07/01/07)
       A Probability Model: The Discrete Case (2.4-2.5) (revised 12/11/08)
       Elementary Combinatorics (2.6) (revised 12/11/08)
       Conditional Probability (2.7)  (revised 09/17/07)
       Independence (2.7)  (revised 09/17/07)
       Some Laws of Probability (2.8) (revised 02/04/09)
             Solutions to Examples in Section 2.8 Notes  (revised 12/11/08)
       Calculating Probabilities: Event (De)Composition Method (2.9) (revised 12/11/08)
       Law of Total Probability; Bayes' Theorem (2.10) (revised 02/09/09)
             Solution to Example 2.100 in Section 2.10 Notes (revised 12/12/08)
             Generalization of Example on Slide 6 in Section 2.10 Notes (revised 12/12/08)
  
             Review of Probability Definitions and Formulas (revised 09/24/07)

Chapter 3 - Discrete Random Variables
       Definition and Probability Distribution (3.2) (revised 02/09/09)
       Expected Value (3.3)  (revised 02/17/09)
             A Physicist's View of the Mean (revised 09/28/06)
       The Binomial Distributions (3.4) (revised 12/14/08)
       The Geometric Distributions (3.5)  (revised 12/14/08)
             Formulas Related to the Geometric Series (revised 10/6/04)
       The Negative Binomial Distributions (3.6) (revised 10/10/07)
       The Hypergeometric Distributions (3.7) (revised 10/08/06)
             Solution to Last Example in Section 3.7 Notes (revised 09/15/07)
             Approximating a Hypergeometric by a Binomial (revised 10/08/04)
       Discrete Uniform Distributions (revised 09/30/05)
       The Poisson Distributions (3.8) (revised 02/18/09)
       Moment-Generating Functions (3.9) (revised 12/15/08)
       Tchebysheff's Theorem (3.11) (revised 01/24/09)
             Additional Example (3.11) (revised 09/16/07)

Chapter 4 - Continuous Random Variables
       Definition and Probability Distribution (4.2) (revised 03/21/09)
             Additional Examples (4.2) (revised 03/21/09)
             Piecewise Functions on the TI-83/84 (revised 10/21/07)
       Expected Value (4.3) (revised 12/15/08)
             Proof of Theorem on Expectations (4.3) (revised 12/15/08)
       Continuous Uniform Distributions (4.4) (revised 03/23/09)
       Normal Distributions (4.5) (revised 12/15/08)
             Linear Interpolation (revised 03/24/09)
       Gamma & Exponential Distributions (4.6) (revised 03/29/09)
             Gamma-Poisson Relation (4.6) (revised 11/01/07)
       Beta Distributions (4.7) (revised 02/12/09)
       Moment-Generating Functions (4.9) (revised 12/15/08)

Chapter 5 - Multivariate Probability Distributions
       Bivariate Distributions (5.2) (revised 04/05/09)
       Marginal and Conditional Distributions (5.3) (revised 03/25/09)
             Conditional Distributions (revised 12/24/08)
       Independence (5.4) (revised 03/25/09)
       Expected Values of Functions of Random Variables (5.5-5.6) (revised 12/23/08)
       Covariance (5.7-5.8) (revised 03/30/09)
       The Multinomial Distributions (5.9) (revised 03/30/09)
       Conditional Expectations (5.11) (revised 11/22/07)

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