Find the probability mass function (PMF) of L A source of informatio.pdf
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The document discusses a probability mass function (pmf) for a source generating symbols from a five-letter alphabet with specified probabilities. It outlines how these symbols are encoded into binary codes, detailing the relationship between the lengths of the codes and their probabilities. The final pmf of the code length 'l' includes values for l = 0, 1, 2, and 4 with corresponding probabilities.
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Find the probability mass function (PMF) of L A source of informatio.pdf
- 1. Find the probability mass function (PMF) of L A source of information randomly generates symbols from a five letter alphabet {a, b, c. d, e}. The probability of each symbol is as follows: P(a) = 1/2; P(b) = 1/4; P(c) = 1/8; P(d) = 1/16; and P(e) = 1/16. These symbols are now encoded into binary codes using the scheme shown below. Let the random variable L denote the length of the binary code (for example, the length of the binary code for the symbol c is 3 bits). Find the probability mass function (PMF) of L. Solution PMF of L: L can take value 1, 2, 3, 4. For L=0, P(L=0)=1/2 For L=1, P(L=1)=1/4 For L=2, P(L=2)=1/8 For L=4, P(L=4)=(1/16)+(1/16)=1/8