Question

In: Statistics and Probability

Suppose (X1,⋯,X8)∼(X1,⋯,X8)∼ Multinomial(n,p1,⋯,p8n,p1,⋯,p8). (a) Find the joint distribution of (X1,X3+X5)using the MGF method. (b) Find the...

Suppose (X1,⋯,X8)∼(X1,⋯,X8)∼ Multinomial(n,p1,⋯,p8n,p1,⋯,p8).

(a) Find the joint distribution of (X1,X3+X5)using the MGF method.

(b) Find the conditional probability function of X1|X1+X3+X5=t. Be sure to specify the support sets for both (a) and (b).

Expert Solution

Answer:

Given that:

Suppose

a) Find the joint distribution of using the MGF method

of

Let

Since

Then which is mgf of binomial (n,p)

From uniqueness property of mgf

The pmf of Y is

b)

Find the conditional probability function of . Be sure to specify the support sets for both (a) and (b).

Taking in (1) using uniqueness property of mgf

We say that

orchestra answered 1 year ago

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