My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 24th, 2017, 08:21 PM   #1
Newbie
 
Joined: Aug 2013

Posts: 16
Thanks: 0

(Brownian Motion) Proving that a random variable X is normal?

I have attached the question below!
So given that W(t) is a Brownian motion, how do you prove X=W(a)+W(b) is normal?

I know it must satisfy this condition: that W(t)-W(s)~N(0,t-s).
My initial thought process: X(t)-X(s)=(W(t)+W(t))-(W(s)+W(s))=2(W(t)-W(s)), but since the interval is 0<a<b, I'm pretty sure the variable substitutions I've done is incorrect.
Is my approach to this problem incorrect? Are the W(a)+W(b) just constants? But that would entail that (W(a)+W(b))-(W(a)+W(b))=0? Sorry, I don't think I am grasping the concepts very well.

I would appreciate any pointers on how to solve this problem!
Attached Images
File Type: jpg Untitled.jpg (14.5 KB, 11 views)

Last edited by facebook; February 24th, 2017 at 08:39 PM.
facebook is offline  
 
February 24th, 2017, 08:31 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 1,653
Thanks: 840

how are we supposed to read that image?
romsek is online now  
February 24th, 2017, 08:38 PM   #3
Newbie
 
Joined: Aug 2013

Posts: 16
Thanks: 0

Hi, sorry I've corrected the image! The original file got downscaled, I did not anticipate image compression, my apologies
facebook is offline  
February 26th, 2017, 03:33 PM   #4
Global Moderator
 
Joined: May 2007

Posts: 6,397
Thanks: 546

You must show W(a)+W(b)-W(a-c)-W(b-c) is normal. The mean = 0, but I am not sure what the variance is.
mathman is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
brownian, motion, normal, proving, random, variable, variance



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Max Transformation of a normal distributed random variable hansherman Advanced Statistics 0 February 6th, 2014 05:25 AM
Let Z be a standard normal random variable Exfactor Algebra 1 January 13th, 2014 10:30 PM
Standard Normal Random Variable Ethnikation Algebra 0 November 8th, 2012 02:58 AM
Finding standard normal random variable football Algebra 1 September 11th, 2011 06:25 AM
Standard normal random variable desiclub07 Algebra 3 June 21st, 2010 03:49 PM





Copyright © 2017 My Math Forum. All rights reserved.