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? =
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? =
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
Section13.3: Special Probability Density Functions
Problem 54E
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa420ac02-9353-4fae-9e0a-5b221122383e%2F8b5d7861-8339-43a6-b4b1-100428ca2f6b%2Frzi3yz_processed.png&w=3840&q=75)
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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