Let X1, .., Xn be a random sample of size n from a population with PDF e-1sxs0+1, where 02 1 f(x) = otherwise Let Y, Y, be the corresponding order statistics. a) Find the joint pdf of Y, and Yp. b) Find the joint pdf of S and T where S= and T = Y, - Y,. Remember to describe the transformed domain.

Let X1, .., Xn be a random sample of size n from a population with PDF e-1sxs0+1, where 02 1 f(x) = otherwise Let Y, Y, be the corresponding order statistics. a) Find the joint pdf of Y, and Yp. b) Find the joint pdf of S and T where S= and T = Y, - Y,. Remember to describe the transformed domain.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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Question

Let X1, .., Xn be a random sample of size n from a population with PDF
8 -1sxs0+1, where 0 2 1
otherwise
Let Y, Yn be the corresponding order statistics.
a) Find the joint pdf of Y, and Yp.
b) Find the joint pdf of S and T where S =.
Y;+Y
and T = Y-Y. Remember to
describe the transformed domain.
I20

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