O Prove that √Y is a pivotal quantity. lint: You may use either the Jacobian or Cumulative Function technique to find the istribution of the pivotal quantity. ) Construct a 100(1 - a)% confidence interval (CI) for the unknown parameter 0.

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Question 1
ability density function
Let Y be a single observation from the following prob-
fy(y | 0) =
20y
(1+0y²)²
y > 0,
where > 0 is a parameter.
a) Prove that √Y is a pivotal quantity.
Hint: You may use either the Jacobian or Cumulative Function technique to find the
distribution of the pivotal quantity.
b) Construct a 100(1 - a)% confidence interval (CI) for the unknown parameter 0.
Transcribed Image Text:Question 1 ability density function Let Y be a single observation from the following prob- fy(y | 0) = 20y (1+0y²)² y > 0, where > 0 is a parameter. a) Prove that √Y is a pivotal quantity. Hint: You may use either the Jacobian or Cumulative Function technique to find the distribution of the pivotal quantity. b) Construct a 100(1 - a)% confidence interval (CI) for the unknown parameter 0.
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