ACSC 380 / MATH 480 Handouts
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WMS refers to Mathematical Statistics with Applications, 7th Ed., Wackerly, et al.

Sections 1 & 2
   Review of Probability Definitions and Formulas (pdf 90 KB) (revised 09/02/09)

Computing Probabilities and Expectations by Conditioning
   Computing Probabilities and Expectations by Conditioning (pdf 130 KB) (revised 09/09/09)
   Conditional Expectations (Section 8 & WMS Section 5.11 - pdf 66 KB) (revised 11/22/07)
   Expectation of a Random Nbr of RVs (Excerpted from the above - pdf 30 KB) (revised 11/22/07)
   Conditioning Homework Problems (pdf 44 KB) (revised 08/15/09)
   Conditioning Homework Solutions (pdf 274 KB) (revised 09/08/09)

Section 4
    Hazard Rate (Failure Rate) Functions (page 116, (ii) - pdf 64 KB) (revised 09/23/09)
   Conditional Distribution of X given A (page 117, (vi) - pdf 85 KB) (revised 09/09/09)
   Mixed Distributions (page 111 & WMS Section 4.11 - pdf 138 KB) (revised 09/02/09)
      Mixed Distribution Homework Problems (pdf 88 KB) (revised 08/25/09)
       Mixed Distribution Homework Solutions (pdf 252 KB) (revised 09/20/09)

Section 5
   Topic List (pdf 118 KB) (revised 09/10/09)
   Calculating E[X] Using F(x) (page 139, (iii) - pdf 143 KB) (revised 02/05/07)

Section 6: Frequently Used Discrete Distributions
   Comparison of Parameterizations (pdf 74 KB) (revised 09/23/09)
   Discrete Uniform Distributions (pdf 24 KB) (revised 09/30/05)
   Multinomial Distributions (page 174 & WMS Section 5.9 - pdf 49 KB) (revised 03/30/09)
      Multinomial Distribution Homework Problems (WMS Section 5.9 - pdf 32 KB) (revised 09/12/09)
      Multinomial Distribution Homework Solutions (revised 10/01/09)

Section 7: Exponential Random Variables
   Poisson Processes (pdf 27 KB) (revised 10/16/09)
   Constant Multiples of Exponentials (pdf 67 KB) (revised 02/27/08)

Section 7: Other Continuous Distributions
    Continuous Distributions - Comparison of Parameterizations (pdf 21 KB) (revised 08/30/09)
   Lognormal Distributions (pdf 43 KB) (revised 03/02/08)
   Pareto Distributions (pdf 133 KB) (revised 10/25/09)
      Some Comments on the Pareto (pdf 76 KB) (revised 10/22/09)
   Weibull Distributions (pdf 59 KB) (revised 08/30/09)
   Comments on f(x), F(x), S(x) for Some Distributions (pdf 48 KB) (revised 10/22/09)
   Comments on Problem 6, Page 214 (pdf 67 KB) (revised 10/27/09)

Section 8
   Joint Moment Generating Functions (page 242 - pdf 21 KB) (revised 03/24/08)
   Bivariate Normal Distributions (page 242 - pdf 56 KB) (revised 10/16/09)
   Expectations of Bivariate Uniform Distributions (pdf 92 KB) (revised 10/31/09)

Section 9
   Order Statistics (page 282 & WMS Section 6.7 - useful earlier - pdf 131 KB) (revised 03/18/05)

Transformations of Random Variables (Summary - pdf 274 KB) (revised 3/31/08)
   Math 347/447 Lecture Notes (Section references are to WMS.)
   Available in both PowerPoint and Adobe Acrobat "pdf" formats.
   Click the corresponding icons to download the files.
       The Method of Distribution Functions (6.3) (revised 12/03/07)
       The Method of Transformations - Univariate Case (6.4) (revised 11/29/07)
       The Method of Moment-Generating Functions (6.5) (revised 12/05/07)
       The Method of Transformations - Bivariate Case (6.6) (revised 12/05/07)

Section 10
   Summary of Section 10 (pdf - 38 KB) (revised 11/12/09) 
 

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