I have an exam at school in 2 days and I am stuck on a question from an old paper.I would appreciate some help in this regard. If $x'$ and $y'$ are the deviations of the variables X and Y about the means, $s_1^2$ and $s_2^2$ are the variances of variables $X $ and $Y$,the correlation co-efficien...

I know I am asking a few questions and I apologise for that.However I shall try to read the solutions and know the loopholes in my theory. Here it is: If $u=x\cos \theta+y\sin\theta$ and $v=y \cos \theta-x\sin\theta$. The variables $u$ and $v$ are uncorrelated, then how may I prove that $$\tan 2...

Suppose $u=cx+dy\dots \boxed{1}$ and $v=cx-dy\dots \boxed{2}$ and $r$ is the correlation co-efficient between $x$ and $y$.If $u$ and $v$ are not correlated, then can I prove that $$s_us_v=2cds_xs_y\sqrt{1-r^2}$$ where $s_j$ is the standard deviation of variable $j$? I do not seem to be getting ...