|February 24th, 2017, 08:21 PM||#1|
Joined: Aug 2013
(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!
Last edited by facebook; February 24th, 2017 at 08:39 PM.
|brownian, motion, normal, proving, random, variable, variance|
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