Branching Process

Definition

A Branching Process is a population model where each individual produces $j$ offspring with probability $P_j$.

$X_n$ is the size of the $n$-th generation.

Moments

Moment	Formula
Mean offspring	$\mu ={\sum }_{j=0}^{\infty }j{P}_j$
Expected size at gen $n$	$E[X_n]={\mu }^n$
Variance at gen $n$	$\text{Var}(X_n)={\sigma }^2{\mu }^{n-1}\frac{1-{\mu }^n}{1-\mu }$

Related

• Extinction Probability