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A what is the distribution of n b what is the distribution

Grouping multinomial categories. Suppose that counts (N₁, . . . N_m) are the rum-bets of results in m categories in n repeated trials. So (N₁, . . . N_m) has multinomial distribution with parameters n and

p₁, . . . p_m as in the box above Example 7. Let 1 < i="">< j="">< m.="" answer="" the="" following="" questions="" with="" an="" explanation,="" but="" no="">

a) What is the distribution of N?

b) What is the distribution of N_i + N_j?

c) What is the joint distribution of N_i, and n - N_i -N_j?

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