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Despite a long search I was not able to find a rigorous proof of the fact that a random vector having a multinomial distribution with parameters p (the vector of probabilities) and n (the number of trials) can be written as the sum of n independent random vectors all having a multinomial distribution with parameters p and 1. Can anyone suggest where to look?

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    Use characteristic function to prove it.2012-09-28
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    Actually, I suspect that the result above is needed to derive the characteristic function, so it would be circular.2012-09-28

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