GATE 2014 EC (EC1) – Question 62
A fair coin is tossed until the first head. L is the number of tosses. Find entropy H(L) (bits).
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Correct answer: 1.99 to 2.01
Explanation
For a fair coin P(L=l)=2⁻ˡ for l≥1. Its information content is−log2P=l bits, so H(L)=Σl2⁻ˡ=E[L]. The geometric waiting time has mean1/p=2. Hence **H(L)=2bits**, despite having infinitely many possible values.