7. Suppose that X follows a geometric distribution, P(X = k) = p(1 –- p)*=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.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 8E
icon
Related questions
Question
7. Suppose that X follows a geometric distribution,
P(X = k) = p(1 – p)*=1
and assume an i.i.d. sample of size n.
a. Find the method of moments estimate of
р.
b. Find the mle of p.
c. Is this MLE an unbiased estimator?
d. Find the asymptotic variance of the MLE, .
e. Is the MLE consistent?
Transcribed Image Text:7. Suppose that X follows a geometric distribution, P(X = k) = p(1 – p)*=1 and assume an i.i.d. sample of size n. a. Find the method of moments estimate of р. b. Find the mle of p. c. Is this MLE an unbiased estimator? d. Find the asymptotic variance of the MLE, . e. Is the MLE consistent?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

Answers for c-e 

7. Suppose that X follows a geometric distribution,
P(X = k) = p(1 - p)*-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. Is this MLE an unbiased estimator?
d. Find the asymptotic variance of the MLE, ..
e. Is the MLE consistent?
Transcribed Image Text:7. Suppose that X follows a geometric distribution, P(X = k) = p(1 - p)*-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. Is this MLE an unbiased estimator? d. Find the asymptotic variance of the MLE, .. e. Is the MLE consistent?
Solution
Bartleby Expert
SEE SOLUTION
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,