GATE 2016 EC – Question 58
Consider a discrete memoryless source with alphabet $S = \{s_0, s_1, s_2, s_3, s_4, \ldots\}$ and respective probabilities of occurrence $P = \left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \ldots\right\}$. The entropy of the source (in bits) is ________
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Correct answer: 1.8 to 2.2
Explanation
The symbol $s_k$ has probability $2^{-(k+1)}$, so its information is $k + 1$ bits. The entropy is $H = \sum_{n=1}^{\infty} \frac{n}{2^n} = 2$ bits.