An information source generates symbols at random from a four letter alphabet {a, b, c, d} with probabilities

P(a)=1/2, P(b)=1/4,

P(c)=P(d)=1/8. A coding scheme encodes these symbols into binary codes as follows:

• 0
• 10
• 110
• 111

Let X be the random variable denoting the length of the code, ie, the number of binary symbols

• What is the range of X?
• Sketch the cdfF_X (x) of X and specify the type of X

Find P(X≤1),P(X>1)& P(1≤X≤2)

**Mumbai University > Electronics and Telecommunication Engineering > Sem 5 > Random Signal Analysis

Marks: 10M

Year: May 2016

The information source generates symbols at random from a four letter alphabet {a, b, c, d}, the probability distribution is represented as:

Let X be the random variable denoting the length of the code, ie, the number of binary symbols

Probability mass function (pmf) is given by:

1. Range of X is 1≤X≤3

2. CDF of X

3. X	1	2	3
   P(X)	1/2	1/4	2/8
   Fx(x)	1/2	3/4	1

X is discrete random variable.

1. P(X ≤ 1)= 1/2

   P(X>1)= 1/4+1/4=1/2

   P(1 ≤ X ≤ 2)= 1/2+1/4=3/4