Module 1:Concepts of Random walks, Markov Chains, Markov Processes
Lecture 1:Introduction to Stochastic Process
We already know that if is the random variable (r.v), such that , , then is the distribution function of the random variable (r.v) . Consider a finite collection of random variables (r.v's) in , where . Then the joint distribution of is given by . In case are independent, we have .
In case they are independent and identically distributed, then the following is true. For example and are
independent but not identical, while and are independent and identical, i.e., i.i.d.
is the random variable (r.v), such that 
, 
, then 
is the distribution function of the random variable (r.v) 
. Consider a finite collection of random variables (r.v's) in 
, where 
. Then the joint distribution of 
is given by 
. In case 
are 
.
. For example 
and 
are
and 
are independent and identical, i.e., i.i.d.
