Seg18. The Correlation Matrix

From Computational Statistics (CSE383M and CS395T)
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Skilled problem

problem 1

Random points i are chosen uniformly on a circle of radius 1, and their <math>(x_i,y_i)</math> coordinates in the plane are recorded. What is the 2x2 covariance matrix of the random variables <math>X</math> and <math>Y</math>? (Hint: Transform probabilities from <math>\theta</math> to <math>x</math>. Second hint: Is there a symmetry argument that some components must be zero, or must be equal?)