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XBernoulli(1/2)X \sim \mathrm{Bernoulli}(1/2) and Y=XZY = X \oplus Z with ZBernoulli(0.2)Z \sim \mathrm{Bernoulli}(0.2). Compute RXY(0.05)R_{X\mid Y}(0.05) in bits under Hamming distortion.
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