How to describe a random process?

           As we have observed above that at a specific time is a random variable and can be described by its probability distribution function This distribution function is called the first-order probability distribution function.
           We can similarly define the first-order probability density function   

To describe ,  we have to use joint distribution function of the random variables at all possible values of .  For any positive integer , represents jointly distributed random variables. Thus a random process can thus be described by specifying the joint distribution function .

or th the joint probability density function

If is a discrete-state random process, then it can be also specified by the collection of joint probability mass function