Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 froma distribution having the pdf f(x) = 2x, 0 < x < 1, zero elsewhere. Show thatZ1 = Y1/Y2, Z2 = Y2/Y3, and Z3 = Y3 are mutually independent.

Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 froma distribution having the pdf f(x) = 2x, 0 < x < 1, zero elsewhere. Show thatZ1 = Y1/Y2, Z2 = Y2/Y3, and Z3 = Y3 are mutually independent.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 from
a distribution having the pdf f(x) = 2x, 0 < x < 1, zero elsewhere. Show that
Z1 = Y1/Y2, Z2 = Y2/Y3, and Z3 = Y3 are mutually independent.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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