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    What does mutual information signify between two random variables, X and Y , in the context of information theory?
    Question

    What does mutual information signify between two random variables, X and Y , in the context of information theory?

    A.

    The total amount of entropy of X and Y .

    B.

    The amount of information that X and Y share.

    C.

    The total amount of redundancy of X and Y .

    D.

    The amount of noise that X and Y share.

    Correct option is B

    In information theory, mutual information I(X;Y) measures how much knowing one random variable reduces the uncertainty about the other.Mathematically:I(X;Y)=H(X)H(XY)=H(Y)H(YX)This represents the shared information between X and Y.\text{In information theory, mutual information } I(X;Y) \text{ measures how much knowing one random variable reduces the uncertainty about the other.} \\[8pt]\text{Mathematically:} \\[6pt]I(X;Y) = H(X) - H(X|Y) = H(Y) - H(Y|X) \\[8pt]\text{This represents the \textbf{shared information} between } X \text{ and } Y .​​

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