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Answer key Q2

Scenario: A digital communication system consists of a transmitter with four possible symbols: X = {x1, x2, x3, x4} The receiver observes three possible output symbols: Y = {y1, y2, y3} Due to channel noise, the joint probability distribution P(X,Y) is given below. Rows correspond to x1, x2, x3, x4 and columns correspond to y1, y2, y3. P(X,Y) = [ 0.30 0.05 0.00 ] [ 0.00 0.25 0.00 ] [ 0.00 0.15 0.05 ] [ 0.00 0.05 0.15 ] Questions: 1. Determine the marginal probability distributions P(X) and P(Y). 2. Calculate the entropy of the transmitter H(X). 3. Calculate the entropy of the receiver H(Y). 4. Compute the joint entropy H(X,Y). 5. Determine the conditional entropies H(X|Y) and H(Y|X).