Joint Entropy closed-form analytical solution Differential entropy of a single Gaussian random variable is H(X)=12ln⁡(2πeσ2) What then is the closed-form analytical solution for joint entropy, H(X,Y)?

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Joint Entropy closed-form analytical solution  Differential entropy of a single Gaussian random variable is  H(X)=12ln⁡(2πeσ2)  What then is the closed-form analytical solution for joint entropy, H(X,Y)?

ul2ph3ojc · Accepted Answer

Let (X,Y)∼N(0,K), were K=[σ2ρσ2ρσ2σ2] Then differential entropy is h(X)=h(Y)=12log⁡(2πe)σ2 and joint entropy is h(X,Y)=12log⁡(2πe)2|K| =12log⁡(2πe)2σ4(1−ρ2)

Joint Entropy closed-form analytical solution Differential entropy of a single Gaussian random variable is H(X)=12ln⁡(2πeσ2)...

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