Let X 1 , X 2 , X 3 , , X n be a random sample from the following distribution where 2, 2 is an unknown parameter We define the estimator n as to estimate a Is n an unbiased estimator of b Is n a consistent estimator of c Find the mean squared error (MSE) of n fx(x) Jo (x 2) 0 1 for 0x 1 otherwise...

a To check if n is an unbiased estimator of we need to find the expected value of n and see if it eq ...

Let X 1 , X 2 , X 3 , . . ., X n be a

Question:

Let X₁, X₂, X₃, . . ., X_n be a random sample from the following distribution fx(x) = Jo (x - 2) 0 +1 for 0x 1 otherwise

where θ ∈ [−2, 2] is an unknown parameter. We define the estimator ^Θ_n as n =12X 6

to estimate θ.

a. Is ^Θ_n an unbiased estimator of θ?

b. Is ^Θ_n a consistent estimator of θ?

c. Find the mean squared error (MSE) of ^Θ_n.

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Introduction To Probability Statistics And Random Processes

ISBN: 9780990637202

1st Edition

Authors: Hossein Pishro-Nik

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Question Posted: Nov 01, 2023 01:39 PM

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Let X 1 , X 2 , X 3 , . . ., X n be a

Question:

fx(x) = Jo (x - 2) 0 +1 for 0≤x≤ 1 otherwise

Step by Step Answer:

a To check if n is an unbiased estimator of we need to find the expected value of n and see if it eq...View the full answer

Introduction To Probability Statistics And Random Processes

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