Question

. A multinomial experiment consist of a sequence of n independent and identical trials where the result in each trial is one of possible m different categories. This categorical variable can be represented as an ordinary discrete variable with values in {1, . . . , m} and probabilities {p1, . . . , pm} . Use this setting and explain that merging together some categories so that m is reduced will give a new multinomial distribution. For instance unifying the last two categories. Likewise, explain conditioning in this framework. As an example consider the case when all occurrence of category 1 are known

Answer 1

let the discrete random Nauable x follows multinomial distribution with m values {), -, my let. m value occurs in.., nm) time respectively we with probabilities (pag., pm) Then pirf is P(A, -, nm) = n p p222 - Anh Dina!. nm! of lost two categories are merged then we have (m-1) categories with corresponding occurences ini, nair, Mithm) and probabilities (p. P2, -, Pontifpm) then pmf is Pln,,..,nmythm) = n bn ' _ - (Posthm) nis - mitam) AOA )