32. a. Let X., X be a random sample from a uniform distribution on [0, 0]. Then the mle of is = Y = max(X). Use the fact that Y≤ y iff each X₁y to derive the cdf of Y. Then show that the pdf of Y=max(X) is nyn-1 fx(y) = 0≤ y ≤ 0 Өп 0 otherwise b. Use the result of part (a) to show that the mle is biased but that (n + 1)max(X)/n is unbiased.
32. a. Let X., X be a random sample from a uniform distribution on [0, 0]. Then the mle of is = Y = max(X). Use the fact that Y≤ y iff each X₁y to derive the cdf of Y. Then show that the pdf of Y=max(X) is nyn-1 fx(y) = 0≤ y ≤ 0 Өп 0 otherwise b. Use the result of part (a) to show that the mle is biased but that (n + 1)max(X)/n is unbiased.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 12CR
Related questions
Question
![32. a. Let X., X be a random sample from a uniform
distribution on [0, 0]. Then the mle of is
= Y = max(X). Use the fact that Y≤ y iff each
X₁y to derive the cdf of Y. Then show that the pdf
of Y=max(X) is
nyn-1
fx(y) =
0≤ y ≤ 0
Өп
0
otherwise
b. Use the result of part (a) to show that the mle is
biased but that (n + 1)max(X)/n is unbiased.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe60e14a8-856f-447c-ac90-795ae43e00b4%2Fccb04f75-a63a-4d3a-9640-547b6d5c99d9%2Fj7kao9g_processed.png&w=3840&q=75)
Transcribed Image Text:32. a. Let X., X be a random sample from a uniform
distribution on [0, 0]. Then the mle of is
= Y = max(X). Use the fact that Y≤ y iff each
X₁y to derive the cdf of Y. Then show that the pdf
of Y=max(X) is
nyn-1
fx(y) =
0≤ y ≤ 0
Өп
0
otherwise
b. Use the result of part (a) to show that the mle is
biased but that (n + 1)max(X)/n is unbiased.
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