Some Illustrative Classroom Examples Regarding Sums of Discrete Random Variables With Finite Support

In many probability and mathematical statistics courses the probability generating function (PGF) is typically overlooked in favor of the more utilized moment generating function. However, for certain types of random variables, the PGF may be more appealing. For example, sums of independent, non-neg...

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Bibliographic Details
Published in:The American statistician Vol. 59; no. 3; pp. 258 - 265
Main Author: Terpstra, Jeff T
Format: Journal Article
Language:English
Published: Alexandria, VA Taylor & Francis 01.08.2005
American Statistical Association
Subjects:
Central limit theorem
Classrooms
Coefficients
Dice
Discrete distributions
Distribution theory
Exact sciences and technology
Generating function
Golf
Limit theorems
Mathematics
P values
Polynomials
Probabilities
Probability
Probability and statistics
Probability generating function
Probability theory and stochastic processes
Proportions
Random variables
Sciences and techniques of general use
Software packages
Statistical methods
Statistics
Sums
Teacher's Corner
Theorems
Wilcoxon signed-rank statistic
Wilcoxon test
Generating function
Statistical moment
Dice
Software package
Probability generating function
Probability distribution
Sums
Statistical method
Random variable sum
Discrete distributions
Central limit theorem
Proportion
Proportions
Discrete distribution
Wilcoxon signed-rank statistic
Distribution function
Software
Exact distribution
ISSN:0003-1305, 1537-2731
Online Access:Get full text
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Summary:In many probability and mathematical statistics courses the probability generating function (PGF) is typically overlooked in favor of the more utilized moment generating function. However, for certain types of random variables, the PGF may be more appealing. For example, sums of independent, non-negative, integer-valued random variables with finite support are easily studied via the PGF. In particular, the exact distribution of the sum can easily be calculated. Several illustrative classroom examples, with varying degrees of difficulty, are presented. All of the examples have been implemented using the R statistical software package.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0003-1305
1537-2731
DOI:10.1198/000313005X54234