Probability generating functions
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Probability generating functions. Uniform, discrete distribution
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Let X be a random variable with a uniform discrete distribution. Then [Equation goes here &- download the original to see it.] The probability generating function is [Equation goes here &- download the original to see it.] t, t2, t3, …, tn is a geometric series with first term t, ratio t, and n terms. Hence [Equation goes here &- download the original to see it.] by the result for the sum of a geometric series. Then [Equation goes here &- download the original to see it.] [Equation goes here &- download the original to see it.] [Equation goes here &- download the original to see it.] [Equation goes here &- download the original to see it.]
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Contents of
Probability generating functions
1 Probability generating functions. Introduction.
2 Probability generating functions. Discrete random variable.
3 Probability generating functions. Uniform, discrete distribution
4 Binomial Distribution
5 Geometric Distribution
6 Poisson Distribution
7 The probability generating function of the sum of two independent variables
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