Module 3:Branching process, Application of Markov chains, Markov Processes with discrete and continuous state space
Lecture 9:Branching process
WALD'S EQUATION
Let denotes the number of the off springs of the individual in the generation, such that . One should remember that both number of off springs as well as generation number are non-deterministic.
Expectation
, where are i.i.d random variables (r.v's). Thus
Generalizing we have : .
The equation , where is the sum of random number of random variables is frequently in sequential analysis. Now as , hence one can easily prove that
denotes the number of the off springs of the 
individual in the 
generation, such that 
. One should remember that both number of off springs as well as generation number are non-deterministic.
are i.i.d random variables (r.v's). Thus 
.
, where 
is the sum of random number of random variables is frequently in sequential analysis. Now as 
, hence one can easily prove that 
