**[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

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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