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.
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
