Use the result of Exercise 6.3-10.(a) Find the joint pdf
Chapter 6, Problem 11E(choose chapter or problem)
Use the result of Exercise 6.3-10.
(a) Find the joint pdf of \(Y_{1}\) and \(Y_{n}\), the first and the \(n\)th order statistics of a random sample of size \(n\) from the \(U(0,1)\) distribution.
(b) Find the joint and the marginal pdfs of \(W_{1}=Y_{1} / Y_{n}\) and \(W_{2}=Y_{n}\).
(c) Are \(W_{1}\) and \(W_{2}\) independent?
(d) Use simulation to confirm your theoretical results.
Equation Transcription:
,
Text Transcription:
Y_1
Y_n
U(0,1)
W_1=Y_1/Y_n
W_2=Y_n
W_1
W_2
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