Let the random variable X follow a uniform distribution in the interval [0,0]. Then the density function of X is if 0
Let the random variable X follow a uniform distribution in the interval [0,0]. Then the density function of X is if 0
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.CR: Chapter 13 Review
Problem 29CR
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![Let the random variable X follow a uniform distribution in the interval [0,0]. Then the
density function of X is
if 0<x<0
0, otherwise.
Consider a random sample of size n from this population.
(a) From the likelihood function of , argue that its maximum likelihood estimator is
the nth order statistic (Y₂).
f(x; 0) =
(b) Is the estimator in part (a) unbiased? If not, find an unbiased estimator of and
denote it by ₁. [Hint: Derive the distribution of Y₁-]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17176ae9-b253-442d-89f9-517b049b4c59%2Fc59a144b-a40e-42e8-9884-a13c1e8f5565%2Fo6t9nhj_processed.png&w=3840&q=75)
Transcribed Image Text:Let the random variable X follow a uniform distribution in the interval [0,0]. Then the
density function of X is
if 0<x<0
0, otherwise.
Consider a random sample of size n from this population.
(a) From the likelihood function of , argue that its maximum likelihood estimator is
the nth order statistic (Y₂).
f(x; 0) =
(b) Is the estimator in part (a) unbiased? If not, find an unbiased estimator of and
denote it by ₁. [Hint: Derive the distribution of Y₁-]
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Transcribed Image Text:(e) Show that ₂ = 2X, with X = 1 EX₁, is unbiased for 0.
(d) Obtain the relative efficiency of 2 with respect to ₁.
Solution
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Transcribed Image Text:(e) Show that ₂ = 2X, with X = 1X₁, is unbiased for 0.
(d) Obtain the relative efficiency of 2 with respect to ₁.
Solution
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