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4. Let X1, ..., Xn be i.i.d. with pdf f (x; 0) = 0²xe-0x ,x > 0,0 > 0 a) Write the pdf in an exponential form. b) Find a complete sufficient statistic for 0, if it exists. c) Find the unique minimum variance unbiased estimator for 1/0. d) Find the unique minimum variance unbiased estimator for 0.

4. Let X1, ..., Xn be i.i.d. with pdf f (x; 0) = 0²xe-0x ,x > 0,0 > 0 a) Write the pdf in an exponential form. b) Find a complete sufficient statistic for 0, if it exists. c) Find the unique minimum variance unbiased estimator for 1/0. d) Find the unique minimum variance unbiased estimator for 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. Let X1, ..., Xn be i.i.d. with pdf f (x; 0) = 0²xe-0x ,x > 0,0 > 0 a) Write the pdf in an exponential form. b) Find a complete sufficient statistic for 0, if it exists. c) Find the unique minimum variance unbiased estimator for 1/0. d) Find the unique minimum variance unbiased estimator for 0.
Transcribed Image Text:4. Let X1, ..., Xn be i.i.d. with pdf f (x; 0) = 0²xe-0x ,x > 0,0 > 0 a) Write the pdf in an exponential form. b) Find a complete sufficient statistic for 0, if it exists. c) Find the unique minimum variance unbiased estimator for 1/0. d) Find the unique minimum variance unbiased estimator for 0.
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