Question

An event has 4 possible outcomes with probabilities 1/2, 1/4, 1/8, 1/16. What will be the rate of information if there are approximately 24 outcomes/second possible?
1. 78 bits/sec
2. 3 bits/sec
3. 39 bits/sec
4. 6 bits/sec

Answer 1

Correct Answer - Option 3 : 39 bits/sec

Concept:

Information associated with the event is “inversely” proportional to the probability of occurrence.

Entropy: The average amount of information is called the “Entropy”.

\(H = \;\mathop \sum \limits_i {P_i}{\log _2}\left( {\frac{1}{{{P_i}}}} \right)\;bits/symbol\)

Rate of information = r.H

Calculation:

Given: r = 24 outcomes/sec

\(P_1=\frac{1}{2}\), \(P_2=\frac{1}{ 4}\), \(P_3=\frac{1}{ 8}\) and \(P_4=\frac{1}{ 16}\)

\( H = \frac{1}{2}{\log _22} + \frac{1}{4}{\log_24};+ \frac{1}{8}{\log_28};+ \frac{1}{16}{\log_216};\)

H = 1.625 bits/outcome

∴ Rate of information = r.H

Rs = 24 x 1.625

Rs = 39 bits/sec