0
$\begingroup$

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

$\endgroup$
  • 1
    $\begingroup$ 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/… $\endgroup$ – Peter Franek Mar 20 '16 at 8:40
0
$\begingroup$

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: $$\mbox{cov}[X+Y,X-Y] = \mbox{cov}[X,X]+\mbox{cov}[Y,X]-\mbox{cov}[X,Y]-\mbox{cov}[Y,Y].$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.