Solution Found!
Suppose that X follows a geometric distribution, P(X = k)
Chapter , Problem 7(choose chapter or problem)
Suppose that X follows a geometric distribution,
\(P(X=k)=p(1-p)^{k-1}\)
and assume an i.i.d. sample of size n.
a. Find the method of moments estimate of p.
b. Find the mle of p.
c. Find the asymptotic variance of the mle.
d. Let p have a uniform prior distribution on [0, 1]. What is the posterior distribution of p? What is the posterior mean?
Questions & Answers
QUESTION:
Suppose that X follows a geometric distribution,
\(P(X=k)=p(1-p)^{k-1}\)
and assume an i.i.d. sample of size n.
a. Find the method of moments estimate of p.
b. Find the mle of p.
c. Find the asymptotic variance of the mle.
d. Let p have a uniform prior distribution on [0, 1]. What is the posterior distribution of p? What is the posterior mean?
ANSWER:Step 1 of 6
Given:
The variable X follows the geometric distribution with probability mass function as,
