July 29, 2022# What Is a Random Process With Examples?

## What is a random process?

### Example of a random process and a random variable

## Type of random processes

**Note**: donโt fright out over the equation or formulas present in this article as we are to explain each bit by bit.

**A random process** is also termed as a stochastic process and it is a process in which consist of several random variables over time. So you might ask what is a random variable?

*A random variable* is a variable with set of random numbers. Here is what I mean using an example.

Let us take the weather temperature throughout the day in New York as an example. As you can see the graph is showing how the weather changes through the day (or over a 24-hour time period).

At t_{1} we assume it is 5am in the morning, t_{2} is 11am in the morning and t_{3} is 3pm in the afternoon.

Now at t_{1} we assume the value of the temperature in degree is x_{1} = 42^{o}, at t_{2} the value is x_{2} = 47^{o} and at t_{3} the value is x_{3} = 47^{o}.

Those values in degree are the values we take at random time and we can combine them together into a variable called random variable.

This random variable as it changes with time then it is termed as random process.

In essence, random variable is associated with values and it is denoted as (capital x) X which contain (small x which are the values at random) and for our temperature example, we have 3 small xโs (x_{1}, x_{2} and x_{3})

so therefore, X (random variable) = {x_{1}, x_{2}, x_{3}}

Now for the random process, it is denoted as (capital X of t) X(t) since it is associated with time.

Therefore, X(t) = {x_{1}(t), x_{2}(t), x_{3}(t)}.

**Strict sense stationary random process**
A random process is said to be strict sense stationary or simply stationary if none of its statistics is affected by a shift in time origin. i.e. the occurrence of a function x(t1) at t1 is same at x(t2) when there is a shift from 1 to 2.

**Wide sense random process**
A random process is said to be wide sense stationary if two of its statistics (mean and autocorrelation) is not affected by a shift in time origin or do not vary with a shift in time.