# find E[(X-Y)^2] difficult to work out

• Nov 3rd 2010, 09:43 AM
eleahy
find E[(X-Y)^2] difficult to work out
if x,y are independent, identically distributed r.v.-s with mean u and variance sigma^2 , find E[(X-Y)^2].

have tried but dont know how you could use x-y
• Nov 3rd 2010, 10:09 AM
Dinkydoe
$\displaystyle E[(X-Y)^2]= E[X^2-2XY+Y^2]= E[X^2]-2E[XY]+E[Y^2]$

Now use that E[XY]=E[X]E[Y] ...since X,Y are independant.
• Nov 3rd 2010, 10:50 AM
eleahy
confused
im a little confused..... i thought the question asked to find that formula using the fact mean is u and variance is sigma squared. Im probably wrong just dont know how to finish question ...thanks so much for taking time!!!
• Nov 3rd 2010, 12:00 PM
harish21
$\displaystyle E(X) = \mu_{x}$

$\displaystyle Var(X) = E[X^2] - (E[X])^2 = E[X^2] - \mu_{x}^2$
• Nov 3rd 2010, 12:26 PM
eleahy
Ok trying figure this out I can't figure how you get to E(x-y)^2 I'm not sure am I just missing something simple or how you get it. Workin on it but getting no where. Is E(x-y)^2 a specific formula??
• Nov 3rd 2010, 12:49 PM
harish21
Look at post no. 2 by DinkyDoe. It has already been found out for you!
• Nov 3rd 2010, 12:51 PM
eleahy
He seemed to multiply out then simplify , do I use your info before this I'm failing to see the connection sorry thanks for helpin ;)
• Nov 3rd 2010, 01:07 PM
harish21
Follow his instructions first, and then use my info!