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7. Suppose that X follows a geometric distribution,and assume an i.i.d. sample of size nc. Find the asymptotic variance of the mle.d. Let p have a uniform prior distribution on [0, 1. What is the posterior distri-bution of p? What is the posterior mean?

Question
7. Suppose that X follows a geometric distribution,
and assume an i.i.d. sample of size n
c. Find the asymptotic variance of the mle.
d. Let p have a uniform prior distribution on [0, 1. What is the posterior distri-
bution of p? What is the posterior mean?
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7. Suppose that X follows a geometric distribution, and assume an i.i.d. sample of size n c. Find the asymptotic variance of the mle. d. Let p have a uniform prior distribution on [0, 1. What is the posterior distri- bution of p? What is the posterior mean?

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Step 1

c.

The asymptotically variance of mle:

The mle of p is given below:

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Step 2

The asymptotically variance of mle is 1/I(p) is given below:

 

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Step 3

d.

Computing posterior distribution of p and posterior mean:

The posterior distrib...

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