Probability generating functions
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Geometric Distribution
The discrete random variable X follows the Geometric distribution when it arises from the application of possibly infinite trials to a situation where at each trial there is a probability p of a success and q = 1-p of a failure. The trials are repeated until a success is obtained. The probability that r trials will be necessary until a success is obtained is given by [Equation goes here &- download the original to see it.] We write [Equation goes here &- download the original to see it.] The probability generating function for the Geometric distribution is [Equation goes here &- download the original to see it.] This is, not surprisingly, a geometric series with first term pt and ratio qt. The sum to infinity is [Equation goes here &- download the original to see it.] 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.]
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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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