Question

what's meaning of covariance (x,x)= var(x)? I know covariance describes the relationship between x and y and variance tells us how much the vaules of x vary from the mean. I'm really confused. what is relationship between x and x exactly and what do I mean by saying the relationship could be calculated be finding variance of x​

Answer 1

The covariance of two random variables X and Y is defined as

Cov(X, Y) = E[(X - E[X]) (Y - E[Y])]

where E is expectation.

If we replace Y with X, then this reduces to just the variance of X, which is defined as

Var(X) = E[(X - E[X])²]