University of Birmingham - Probability & Statistics (Solutions)

Statistics, often regarded as a distinct scientific discipline rather than a branch of mathematics, is the study of data and uncertainty, enabling us to draw meaningful conclusions and make informed decisions. It plays a crucial role in designing experiments, determining data collection strategies, and solving practical problems, such as assessing health risks associated with living near electricity pylons or establishing safety testing schedules for aircraft components. This module, Probability & Statistics - introduces fundamental concepts in probability and statistics, including axiomatic probability theory, Bayes’ Theorem, and key probability models like the binomial, Poisson, and normal distributions. It explores the properties of expectation and variance, the significance of the Weak Law of Large Numbers, and the Central Limit Theorem, leading to essential statistical techniques such as inference, point estimation, confidence intervals, and hypothesis testing.