– Stochastic Course Notes

## 1. Definition

Consider a population

- Each individual produces j new offspring each period with probability . Key assumption: This distribution is constant over time.
- Assume that for all j (i.e., the problem is not deterministic)
- Let be the size of the population at period n

## 2. Number of Population in the n-th Generation

## 3. Probability of Die Out

__Analysis__

__Example__## 4. Example: Family Genetics

**Problem:**

__Solution:__