Answered: Suppose Y1,Y2,··· ,Yn are i.i.d.…

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

Suppose Y1,Y2,··· ,Yn are i.i.d. continuous uniform(0,1) distributed.
(a) Prove that the kth-order statistic, Y(k), has Beta distribution with α = k and β = n−k+ 1.
(b) What is the distribution of the median of Y1,Y2,··· ,Yn when n is an odd integer?
(c) Find the joint density of the middle two of Y(1),Y(2),··· ,Y(n) when n is an even integer

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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