Using Venn diagrcuns(维拉图) we can see that mutual i
Using Venn diagrcuns(维拉图),we can see that mutual information common to three random variable X,Y and Z should be defined by I(X;Y;Z)=I(X;Y) - I(X;Y|Z) This quantity is symmetric in X,Y and Z,despite the preceding asymmetric define.Unfortunately,I(X;Y;Z)is not nesessarily nonnegative.Find X,Y,Z such that I(X;Y;Z)<0,and Prove the following two identities: I(X;Y;Z)=H(XYZ) - H(X) - H(Y) - H(Z)+I(X;Y)+I(Y;Z)+I(Z;X) I(X;Y;Z)=H(XYZ) - H(XY) - H(YZ) - H(ZX)+H(X)+H(Y)+H(Z) The first identity can be understood using the Venn diargram analogy for entropy and mutual lnlormatlon.The second identity follows easily from the first.
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