Multinomial Distribution

A random variables X1, X2, ..., Xn have a multinomial distribution and it is referred to as a multinomial random variable if and only if their joint probability distribution is given by
\[ M({\bf x}; {\bf p}, n ) = \Pr \left[ X_1 = x_1 , \ldots , X_m = x_m \right] = \binom{n}{x_1, x_2 , \ldots , x_m} p_1^{x_1} p_2^{x_2} \cdots p_m^{x_m} , \]
where M(x; p, n) = M(x1, x2, ..., xm; p1, p2, ... , pm; n) with xi ∈ [0..n], \( n= \sum_{i=1}^m x_i , \quad \sum_{i=1}^m p_i =1 . \)
R has two dedicated commands to generate multinomially distributed random number vectors and compute multinomial probabilities. size and prob: