Covariance

[urvashi]

How to compute cov (x+y,x-y )

[Akash]

Imagine 2 new random variables u=x+y and v=x-y.
avg(u)=avg(x)+avg(y) avg(v)=avg(x)-avg(y)
Var(u)=var(x) +var(y)  Var(v)=var(x) +var(y)

Cov(u,v) is calculated using above. Does that help?

[Dr. Strange]

Var(u)=var(x) +var(y) + 2 cov(x,y)

[Amit Goyal]

cov(X+Y,X-Y)
= cov(X,X) + cov(X,-Y) + cov(Y,X) + cov(Y,-Y)
= cov(X,X) - cov(X,Y) + cov(Y,X) - cov(Y,Y)
= cov(X,X) - cov(Y,Y)
= var(X) - var(Y)

[Akash]

Shit I always forgot the 2xy term.

[urvashi]

Thank you