What Multinomial distribution is
The multinomial distribution is a type of probability distribution used to describe the results of a multi-category event. It is used to model the probability of observing a certain combination of outcomes in a set of trials.
Steps for Multinomial Distribution:
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Define the number of categories (k) and the number of trials (n).
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Assign a probability of success (p) to each category.
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Calculate the probability of observing a certain category combination using the equation: P(X1=x1,X2=x2,…Xk=xk)=(n!/(x1!x2!…xk!)) (p1^x1)(p2^x2)…(pk^xk)
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Calculate the probability of observing any combination of categories by summing the probabilities of all possible combinations.
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Determine the mean and variance of the multinomial distribution.
Examples
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A multinomial distribution can be used to model the number of successes in multiple categories, such as the number of heads when flipping three coins.
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A multinomial distribution can be used to model the number of occurrences of each categorical outcome in a sample, such as the number of red, green and blue marbles in a bag.
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A multinomial distribution can be used to model the number of successes for each category in a survey, such as the number of people who answered “Yes”, “No” and “Maybe” to a question.