20.4.5  Multinomial distribution

If X follows a multinomial probability distribution with P= [p₀,p₁,…,p_j] (where p₀+⋯+p_j=1), then for K=[k₀,…,k_j] with k₀+⋯+k_j=n, the probability that X=K is given by

The multinomial command computes the density function for the multinomial distribution.

• multinomial takes three arguments:
  • n, an integer.
  • P=[p₀,p₁,…,p_j], a probability vector (i.e., p_k≥ 0 for all k and p₀+⋯+p_j=1).
  • K=[k₀,…,k_j], a list of integers with k₀ + …+k_j=n.
• multinomial(n,P,K) returns the probability that X=K, given in (3).

You will get an error if k₀+⋯+k_j is not equal to n, although you won’t get one if p₀+⋯+p_j is not equal to 1.

Example

Suppose you make 10 choices, where each choice is one of three items; the first has a 0.2 probability of being chosen, the second a 0.3 probability and the third a 0.5 probability. The probability that you end up with 3 of the first item, 2 of the second and 5 of the third will be: