[After reading this module, students should be familiar with probability distributions most important to modelling in the life and social sciences; Uniform, Normal, Poisson, Exponential, Gamma, Negative Binomial, and Binomial.]

Contents:
Introduction
Probability distributions in general
Probability density functions
Mean, variance, and moments of probability density functions
Mean, variance, and moments of a sample of random numbers
Uncertainty on sample mean and variance, and hypothesis testing
The Poisson distribution
The Exponential distribution
The memory-less property of the Exponential distribution
The relationship between the Exponential and Poisson distributions
The Gamma and Erlang distributions
The Negative Binomial distribution
The Binomial distribution

Introduction

There are various probability distributions that are important to be familiar with if one wants to model the spread of disease or biological populations (especially with stochastic models).  In addition, a good understanding of these various probability distributions is needed if one wants to fit model parameters to data, because the data always have underlying stochasticity, and that stochasticity feeds into uncertainties in the model parameters.  It is important to understand what kind of probability distributions typically underlie the stochasticity in epidemic or biological data.
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