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Math and science::INF ML AI

Covariance matrix

Let X and Y be two random variables. The covariance between X and Y is defined as:

Cov[X,Y]:=E[(XE[X])(YE[Y])]=[...]

Let the vector Z be defined like so: Z:=[XY]. Thus, Z is a vector of random variables.

The covariance matrix for Z is defined as:

Cov[Z]:=E[(ZE[Z])(ZE[Z])T]=[...]

Where the expectation is an elementwise operation. The covariance matrix is a result of a matrix multiplication of two vector-like matrices, which produces a 2x2 matrix. (Yes, it is valid!).