# covariance and correlation of x and y

Given that the independent random variables $X$ and $Y$ have variance $36$ and $16$ respectively. Find (i) $Var(X + Y)$ (ii) $Var(X – Y)$ (iii) the correlation coefficient between $(X + Y)$ and $(X – Y)$ I found the answers for the first $2$ parts which is basically the addition of the variances and that is $52$. But for the third part $\text{correlation}= Cov(x+y,x-y)/(stdx.stdy)$ how do i find $Cov(x+y,x-y)$ because $cov(x,y)=E(XY)-E(X)E(Y)$. how do i find the expectations as they are not given. Your help will be much appreciated

• Welcome to math.SE, Please, have a look at the link down for some hints on writing math-equations. It is usually expected that you include some of your own attempts to solve the problem. Do you know that "independent" implies zero covariance? meta.math.stackexchange.com/questions/5020/… – Peter Franek Mar 20 '16 at 8:40

The covariance of two independent r.v is equal to zero, hence $\mbox{cov}[X,Y] = 0$. To find the answer to your question use: $$\mbox{cov}[X+Y,X-Y] = \mbox{cov}[X,X]+\mbox{cov}[Y,X]-\mbox{cov}[X,Y]-\mbox{cov}[Y,Y].$$