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Multinomial Distribution Calculator (with Examples)


The multinomial distribution calculator allows us to calculate the probabilities associated with random variables obeying the multinomial distribution. Let Xi (i=1,2,…,k) denote the random variables. Let pi denote the probability that outcome ‘i’ occurs in a particular trial. Suppose n successive trials are conducted. The probability mass function is given as,

Probability Distribution function of the Multinomial distribution

The calculator below allows us to calculate the associated probabilities by substituting the values of pi (Probability in the first column) and xi (Frequencies in the second column).

Outcome Probability Frequency
Outcome 1
Outcome 2
Outcome 3
Outcome 4
Outcome 5
Outcome 6
Outcome 7
Outcome 8
Outcome 9
Outcome 10

Multinomial Probability: 0.007454

Probabilities must add up to 1. They currently add up to 0.359

For example, if we put, p1 = 0.2, p2 = 0.7 and p3 = 0.1 and,

x1=4 ; x2 = 5 ; x3 = 3 then,

Multinomial Probability = 0.007454

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