Probability and Statistics

Module aims

The aim of this course is to equip students to use probability as a formalism for handling uncertainty, to design simple probability models for prediction, to make basic statistical analyses of data, and to critically assess and interpret others' analyses.

Learning outcomes

By the end of the course, a student should have the ability:

•     To describe a probability space.
•     To define and use random variables.
•     To distinguish and appropriately apply discrete and continuous random variables.
•     To design simple probability models and estimate their parameters from data.
•     To construct confidence intervals.
•     To perform hypothesis tests and draw scientific conclusions.

Practical Skills

• Understand and solve simple probability problems
• Apply estimation and testing procedures.

Transferable Skills

•     To relate real-world problems and systems to probability and statistics.
•     To comfortable communicate probability and statistics.

Module syllabus

Part 1: Probability

Notions of probability: axioms, conditional probability, simple applications.
Discrete random variables and their probability distributions: Bernoulli, geometric, binomial, Poisson; basic properties and applications; probability generating function.
Continuous  random variables and their probability distributions: uniform, negative exponential, Normal; basic properties and applications; Central Limit Theorem; moment generating function and Laplace transform.
Joint random variables.

Part 2: Statistics

Estimation
Hypothesis Testing
Bayesian inference

Pre-requisites

A basic understanding of mathematical methods, at the level of C145.

Teaching methods

Lecture slides will be made available to students in batches over the term online via CATE. The material is supplemented with problem sheets, which students need to answer diligently in order to be able to apply what they have seen in lectures. Selected questions will be assessed as coursework throughout the course.

Assessments

•  Assessed coursework, set in small, regular amounts throughout the course.
•  Exam in the summer term.