Find the sampling distribution for Y2, the 2nd order statistic for random samples ofsize n=4 taken without replacement from the finite population consisting of the first6 positive integers (1,2,3,4,5,6).

Answered: Find the sampling distribution for Y2,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Find the sampling distribution for Y2, the 2nd order statistic for random samples of
size n=4 taken without replacement from the finite population consisting of the first
6 positive integers (1,2,3,4,5,6).

Expert Solution

Step 1 Introduction

Given that the population consists of the first 6 positive integers (1,2,3,4,5,6), from which we draw samples of size n=4 without replacement.

Thus the total number of ways we can draw these samples of size 4 are ${}^{6}{c_{4} = 15}$ .

Y₂, the 2^nd order statistic for the random sample is nothing but the second smallest number among the 4 numbers.

The possible values Y₂ can take are 2,3 and 4. Y₂ cannot take values 1 and 6 because:

if Y₂=1, then there needs to be a value less than 1 in the sample, which is not possible
if Y₂=5 or 6 then there are a value less than 1 in the sample, which is not possible

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