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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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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?
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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?
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