Question

What is the random process? Write a random process report on 15 pages .

Answer 1

A random process is a time-varying function that assigns the outcome of a random experiment to each time instant: X(t).

A random process is a time varying function.
Eg: A signal.

For fixed t: a random process is a random variable.

A random process X(t) is used to explain the mapping of an experiment which is random with a sample space S which contribute to sample functions X(t,lambda_​i).For every point in time t​​​​1,X(t_{​​​​​​j}) is

A random variable.

* t represents time and it can be discrete or continuous.

* The range of t can be finite, but generally it is infinite. It means the process contains infinite number of random variables.

Random Process can be continuous or discrete Real random process also called stochastic process.
Eg: Noise source

Deterministic And Non-Deterministic Random Process:

When the future values of any sample function are predicted depending on the knowledge of the past values, then the random process is known as deterministic random process.

A random process is the combination of time functions, the value of which at any given time cannot be pre determined. So it is known as non deterministic process.

Ergodic and Nonergodic Random Processes:

Ergodic:

Every number of the random process has the same statistical behavior as the entire random process.

* The statistical behaviour can be determined by examining only one sample function.
Such processes are called ergodic.

* The mean values are determined by time averages.

* Ergodic processes are also stationary processes.

Nonergodic:

* It is opposite to ergodic,

* There is a possibility that stationary processes can be non ergodic.