Let X₁, , Xn be a random sample from a large population following a uniform distribution over [0, K]. We do not know K and we want to estimate it. Define - 1/(X₁) ·(X₁ +... + Xn), n (a) What is the expected value of X¡ (for any i = 1,...,n)? (State it as a function of K) (b) Find E(X). (c) Is X an unbiased estimator of K? =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Let X₁,..., X₁ be a random sample from a large population following a uniform
distribution over [0, K]. We do not know K and we want to estimate it. Define
1
x = -=- (X₁
X
+
+ Xn),
n
(a) What is the expected value of X; (for any i = 1,...,n)? (State it as a function of K)
(b) Find E(X).
(c) Is X an unbiased estimator of K?
Transcribed Image Text:Let X₁,..., X₁ be a random sample from a large population following a uniform distribution over [0, K]. We do not know K and we want to estimate it. Define 1 x = -=- (X₁ X + + Xn), n (a) What is the expected value of X; (for any i = 1,...,n)? (State it as a function of K) (b) Find E(X). (c) Is X an unbiased estimator of K?
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