What is a stochastic process?
It is a process in which a group of random variables, distributed over a period of time t, and is measured on a same sample space is indexed.
During this process we see that the random variable X1 changes over a period of time t i.e. from t1 to tn. But in case of identical random variable the distribution of random variable remains same over time t. Another important point to remember while dealing with stochastic process is that it is important to mention the period in which the random variable is taking place. The spacing between different periods of time may be equal or may vary according to the environment on which this process is taking place.
These examples will make the concept clear:
Thus, both the example proves that distribution of random variable may differ with time or may stay same over the same period.