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Given a random variable X that produces real numbers x with a distribution p(x).

The random variable Y is generated from X by the signum function; i.e., y=1 for x>=0 and y=-1 for x<0.

How can I calculate the covariance of X and Y in general? And, if there is no general solution, does a solution exist if p(x) is a gaussian distribution with mean zero?

Slainte!

Hanspeter