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Let U and V be two independent and identically distributed random variables such that P(U < 0) = P(V < 0) = 1/2. The entropy H(U | V) in bits is

1. 3/4
2. 1
3. 3/2
4. log₂3

Correct answer: 1

Solution

The entropy H(U | V) is equal to H(U) since U and V are independent. Given that both U and V are identically distributed with P(U < 0) = 1/2, the entropy of a binary random variable with equal probabilities is 1 bit.

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