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

The calculator below allows us to calculate the associated probabilities by substituting the values of p_{i} (Probability in the first column) and x_{i} (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, p_{1} = 0.2, p_{2} = 0.7 and p_{3} = 0.1 and,

x_{1}=4 ; x_{2} = 5 ; x_{3} = 3 then,

Multinomial Probability = 0.007454