# Modelling and estimation

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Learn about modelling and estimation with a focus on the binomial distribution. Understand probability, notation, and properties. Estimate probabilities and calculate binomial probabilities using maximum likelihood estimation. Gain knowledge on Bernoulli trials and the importance of maximum likelihood estimation.

This free course is concerned with modelling and estimation and looks in particular at the binomial distribution. Section 1 starts by defining probability, introduces relevant notation and briefly discusses basic properties of probabilities. The section concludes by considering some of the general features of and ideas about modelling discrete random variables. Section 2 looks at one particular probability model for discrete data, the binomial distribution. Section 3 investigates how data can be used to estimate the probability of success in a single Bernoulli trial and introduces maximum likelihood estimation.

## Course learning outcomes

After studying this course, you should be able to:

Estimate a probability given data, and calculate a probability when assumptions about the symmetry of an object or situation can be made

Understand how probabilities of outcomes are encapsulated in the probability mass function (p.m.f.) of models for discrete data

Understand the meaning of the term Bernoulli trial, which describes a single statistical experiment for which there are two possible outcomes, often referred to as ‘success’ or ‘failure’

Calculate binomial probabilities

Appreciate that the method of maximum likelihood estimation is an important way of estimating a parameter.

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