Question
Download Solution PDFAn 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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
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