Module 3:Branching process, Application of Markov chains, Markov Processes with discrete and                 continuous state space
  Lecture 10:Application of Markov Chains
 

Variance

Let  be the sum of random number of random variables, i.e., , where  is the random number and  are the random variables which are i.i.d.

Similarly we find the variance

(3.1)

Now , hence

. Using these results and replacing them in (3.1) we have

 as

Thus