Mathematics

Probability and Statistics

Module code: G5146
Level 5
15 credits in spring semester
Teaching method: Lecture, Workshop
Assessment modes: Coursework, Unseen examination

The goal of this module is to further refine your understanding of basic notions of probability and learn how to apply that knowledge to questions of practical importance in statistics. The module will begin by introducing tools to understand the notion of joint statistics - the study of two or more random variables which may be correlated. This will be applied to statistical data sets by means of the method of least squares, or linear regression.

The second part of the module further develops this knowledge in the direction of statistics. We will introduce important distributions in statistics such as the multivariate normal distribution, Chi-square distribution and F distribution, and introduce parameter estimation. You will discuss how this technique was used by the allies during WW2 in the famous German Tank Problem. You will also study an introduction to hypothesis testing and confidence intervals.

Questions we will cover:

  • How many people need to be polled so the outcome of an election is accurately predicted? What if the election is particularly polarising?
  • If somebody says “I am throwing darts randomly on the board”, do they mean that the x and y coordinate of their darts are `random’ or do they mean something else? How can we decide the answer?
  • Is there any relation between the number of storks in the sky and the number of births in the country?

Probability and Statistics continues to build on the knowledge of module G5143 (Introduction to Probability).

Module learning outcomes

  • Select and employ appropriate methods to solve basic problems using vector random variables;
  • Appreciate and understand the multivariate Normal distribution
  • Apply linear regression to data from real-life applications;
  • Use a variety of methods to estimate parameters and perform statistical tests in realistic problems.