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GATE EC 2025 Set 1 — Question 60

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NAT+2 / -0MediumConditional Entropy & Mutual InfoInformation TheoryCommunicationsJoint ProbabilityProbabilityEngineering Mathematics

Communications → Information Theory → Conditional Entropy & Mutual Info

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Question

XX and YY are Bernoulli random variables taking values in {0,1}\{0,1\}. The joint probability mass function of the random variables is given by:
P(X=0,Y=0)=0.06P(X = 0, Y = 0) = 0.06
P(X=0,Y=1)=0.14P(X = 0, Y = 1) = 0.14
P(X=1,Y=0)=0.24P(X = 1, Y = 0) = 0.24
P(X=1,Y=1)=0.56P(X = 1, Y = 1) = 0.56
The mutual information I(X;Y)I(X; Y) is _________ (rounded off to two decimal places).
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