Let a set of random variates , , ..., have a probability function
(1)
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where are nonnegative integers such that
(2)
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and are constants with and
(3)
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Then the joint distribution of , ..., is a multinomial distribution and is given by the corresponding coefficient of the multinomial series
(4)
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In the words, if , , ..., are mutually exclusive events with , ..., . Then the probability that occurs times, ..., occurs times is given by
(5)
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(Papoulis 1984, p. 75).
(6)
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(7)
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The covariance of and is
(8)
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