Entropic Vector - Example

Example

Let X,Y be 2 independent binary random variables with probability of each symbol as one-half. Then

H \left (X \right ) = H(Y) = 1, H(X,Y) = 2

Note that mutual information is then given by

I \left (X;Y \right ) = H(X) + H(Y) - H(X,Y) = 0

This is because X and Y are independent. The entropic vector is thus

v = \left ( 1,1,2 \right )^T

We note that is in as there exists random variables with the entries in the vector as its entropies.

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