My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 22nd, 2011, 04:58 PM   #1
Member
 
Joined: Sep 2007

Posts: 49
Thanks: 0

Uniform distribution of Random variables

Hi, I have a question:
Let X1,X2,...Xn be independent random variables, each having a uniform distribution over (0,1). Let M= max (X1,X2,...,Xn). Show that the distribution function of M, FM(*), is given by FM(x)=x^n. 0<=X<=1.

So I have no problem figuring out the majority part of it, and I worked up to FM(x) = P(X1<=x)*P(X2<=x)*...P(Xn<=x). But I have trouble finding the individual P. However, a friend told me that since it's uniformly distributed from 0 to 1, P(X1<=x)...P(Xn<=x) are each x. But I am still confused at how do you get x? Thanks!
mia6 is offline  
 
February 23rd, 2011, 02:11 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,643
Thanks: 628

Re: Uniform distribution of Random variables

Uniform between 0 and 1 means that the density function = 1 for 0<x<1 and 0 otherwise. Therefore the distribution function is the integral from 0 to x (for x in the range (0,1) of 1.
mathman is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
distribution, random, uniform, variables



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Distribution of the difference between 2 random variables ? nikozm Algebra 1 December 18th, 2013 02:10 PM
Sum of Two Uniform Random Variables Advanced Statistics 0 February 3rd, 2011 07:24 PM
Normal distribution with 2 random variables callkalpa Advanced Statistics 0 May 17th, 2010 07:47 AM
Joint probability distribution of random variables meph1st0pheles Advanced Statistics 1 March 23rd, 2010 06:47 PM
random vectors - uniform distribution begyu85 Algebra 1 March 28th, 2008 05:31 PM





Copyright © 2018 My Math Forum. All rights reserved.