Well from observation we know $E[z] = E[w] = 0$ due to them being periodic.

We also know that $E[x^2]=\sigma_x$ and $E[Y^2] =\sigma_y$.

So then... $Var[z] = E[z^2] - (E[z])^2$ and since $E[z]=0$ $Var[z] = E[z^2] = (x\cos(\theta)+y\sin(\theta))^2$

## Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett