A machines time to fail, T = X+Y. X and Y are independent random variables, with var[X]=var[Y]=10. What is var[T]?

So, as far as I know,
var[T] = var[X+Y] = var[X]+2cov[X,Y]+var[Y].
This gives me 20+2cov[X,Y].

My question, assuming the above is right... is how do I get the cov[X,Y] without more information.

Question

A machines time to fail, T = X+Y. X and Y are independent random variables, with var[X]=var[Y]=10.  What is var[T]?

So, as far as I know,
 var[T] = var[X+Y] = var[X]+2cov[X,Y]+var[Y].
This gives me 20+2cov[X,Y].

My question, assuming the above is right... is how do I get the cov[X,Y] without more information.

anonymous · Answer

nevermind. Just realized that if X and Y are independent, cov[X,Y] = 0.