This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# MultinomialDistribution

 MultinomialDistributionrepresents a multinomial distribution with n trials and probabilities .
• The probability for a vector of non-negative integers , , ..., in a multinomial distribution is .
• The number of trials n can be any positive integer, and can be any non-negative real numbers such that .
Probability density function:
Cumulative distribution function:
Mean and variance:
Covariance:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Covariance:
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 Scope   (7)
Generate a set of pseudorandom vectors that follow a multinomial distribution:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Goodness-of-fit test:
Skewness:
Kurtosis:
Correlation:
Hazard function:
Multivariate marginals do not simplify:
Plot the probability density function of the marginal for fixed values of parameters:
 Applications   (5)
There are two candidates in an election where the winner is chosen based on a simple majority. Each of voters votes for candidate 1 with probability and for candidate 2 with probability , where , so that a voter may choose not to vote for either candidate. When , , the probability of one swing vote is:
Probability that a winner won by one vote:
Probability that candidate 1 wins the election:
Probable outcome of the next election:
Average outcome of an election:
Distribute 5 balls among 3 containers, picking each container with equal probability. Find the probability that no container is empty:
Compute the same probability using SurvivalFunction:
Distribute balls among containers with equal probability. Find the probability that no container is empty for different values of and :
In calling a customer service center, one of three things may happen: the line is busy with probability 0.4, a caller gets the wrong party with probability 0.1, or a caller gets connected to an agent. Find the probability that a caller calling at 6 different times gets a busy signal 4 times and twice connects directly to an agent:
Find the probability that calling at 6 different times, a caller gets the wrong party at least twice:
Simulate 6 calling attempts done at different times:
In a certain city, out of all 911 calls 30% were requesting an ambulance, 15% were requesting the fire department, and the rest were police requests. Find the probability that in the next 10 emergency calls, 2 will ask for an ambulance, 1 for the fire department, and 7 for police:
Simulate the request distribution for the next 100 calls:
Define a multivariate Polya distribution as a parameter mixture of multinomial distribution:
Relationships to other distributions:
A bivariate multinomial distribution is a BinomialDistribution:
A univariate multinomial distribution is a shifted BernoulliDistribution:
MultinomialDistribution is not defined when n is not a positive integer:
MultinomialDistribution is not defined when the elements of p do not sum to 1:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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