APPENDIX EGENERATING FUNCTIONS

DISCRETE DISTRIBUTIONS

Distribution Probability function Range (upper R Subscript upper X) upper E left-parenthesis upper X right-parenthesis upper V left-parenthesis upper X right-parenthesis mgf pgf cf
Bernoulli f left-parenthesis x right-parenthesis equals Start 2 By 2 Matrix 1st Row 1st Column p comma 2nd Column x equals 1 2nd Row 1st Column q equals 1 minus p comma 2nd Column x equals 0 EndMatrix upper R Subscript upper X Baseline equals StartSet 0 comma 1 EndSet p p q q plus p e Superscript t q plus p t q plus p e Superscript i t
Binomial f left-parenthesis x right-parenthesis equals StartBinomialOrMatrix n Choose x EndBinomialOrMatrix p Superscript x Baseline q Superscript n minus x upper R Subscript upper X Baseline equals StartSet 0 comma 1 comma 2 comma ellipsis comma n EndSet n p
Geometric
Negative binomial

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