# /Segment18

1. Random points i are chosen uniformly on a circle of radius 1, and their $(x_i,y_i)$ coordinates in the plane are recorded. What is the 2x2 covariance matrix of the random variables $X$ and $Y$? (Hint: Transform probabilities from $\theta$ to $x$. Second hint: Is there a symmetry argument that some components must be zero, or must be equal?)
$Sin 2. Points are generated in 3 dimensions by this prescription: Choose [itex]\lambda$ uniformly random in $(0,1)$. Then a point's $(x,y,z)$ coordinates are $(\alpha\lambda,\beta\lambda,\gamma\lambda)$. What is the covariance matrix of the random variables $(X,Y,Z)$ in terms of $\alpha,\beta,\text{ and }\gamma$? What is the linear correlation matrix of the same random variables?