probabilty

Introduction:

One of the possible ways
of classifying the signals is: deterministic or random. By random we mean
unpredictable; that is, in the case of a random signal, we cannot with certainty
predict its future value, even if the entire past history of the signal is known. If the
signal is of the deterministic type, no such uncertainty exists.
Consider the signal x t A f t ( ) = cos 2 ( π + θ 1 ). If A, θ and f1 are known,
then (we are assuming them to be constants) we know the value of x( ) t for all t .
( A, θ and f1 can be calculated by observing the signal over a short period of
time).
Now, assume that x(t) is the output of an oscillator with very poor
frequency stability and calibration. Though, it was set to produce a sinusoid of
frequency f f = 1, frequency actually put out maybe f1' where f f f 1 1 1 ' ∈ ± â?? ( ).
Even this value may not remain constant and could vary with time. Then,
observing the output of such a source over a long period of time would not be of
much use in predicting the future values. We say that the source output varies in
a random manner.
Another example of a random signal is the voltage at the terminals of a
receiving antenna of a radio communication scheme. Even if the transmitted

(radio) signal is from a highly stable source, the voltage at the terminals of a
receiving antenna varies in an unpredictable fashion. This is because the
conditions of propagation of the radio waves are not under our control.
But randomness is the essence of communication. Communication
theory involves the assumption that the transmitter is connected to a source,
whose output, the receiver is not able to predict with certainty. If the students
know ahead of time what is the teacher (source + transmitter) is going to say
(and what jokes he is going to crack), then there is no need for the students (the
receivers) to attend the class!