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A fair coin is tossed repeatedly until a 'Head' appears for the first time. Let L be the number of tosses to get this first 'Head'. The entropy H(L) in bits is _____.

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

L is geometric: P(L=k)=(1/2)^k for k>=1. H(L) = -sum (1/2)^k log2((1/2)^k) = sum k(1/2)^k = 2 bits.

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