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

1. ## 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

2. $E[(X-Y)^2]= E[X^2-2XY+Y^2]= E[X^2]-2E[XY]+E[Y^2]$

Now use that E[XY]=E[X]E[Y] ...since X,Y are independant.

3. ## 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!!!

4. $E(X) = \mu_{x}$

$Var(X) = E[X^2] - (E[X])^2 = E[X^2] - \mu_{x}^2$

5. 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??

6. Look at post no. 2 by DinkyDoe. It has already been found out for you!

7. 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

8. Follow his instructions first, and then use my info!