Suppose that the vector x (x, y, z) has a trinomial distribution depending on the index n and the parameter ( , p, ), where p 1, that is Show that this distribution is in the two parameter exponential family p(x ) n x y z p (x y z n)

Question: Suppose that the vector x = (x, y, z) has a trinomial distribution depending on the index n and the parameter = ( ,

Suppose that the vector x = (x, y, z) has a trinomial distribution depending on the index n and the parameter π = (π , p, σ), where π + p + σ = 1, that is

p(x|) n! x!y!z! -*p (x+y+z= n).

Show that this distribution is in the two-parameter exponential family.

p(x|) n! x!y!z! -*p (x+y+z= n).

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