# Biomedical Engineering (MEng)

## Probability and Statistics for Bioengineering

### Module aims

To ensure that all students acquire a solid foundation in probability theory as well as the statistical knowledge and skills required for the advanced years of their Bioengineering programme.

### Learning outcomes

Learning Outcomes - Knowledge and Understanding

• To describe data through statistical quantities such as mean and standard deviation
• To compute probabilities for random variables from probability distributions
• To explain the characteristics of the Gaussian and the Poisson distribution
• To explain the merit and the limitations of the central limit theorem
• To compute confidence intervals
• To test for statistical significance
• To perform linear regression and explain the results

Learning Outcomes - Intellectual Skills

• To compare different statistical quantities to describe data
• To compare and differentiate different probability distributions
• To judge different techniques for statistical tests

Learning Outcomes - Practical Skills

• To apply probabilistic descriptions to real-world data
• To apply statistical tests and regression to experimental data
• To be able to learn about further statistical methods and their applications

Learning Outcomes - Transferable Skills

• To recognize common statistical features in diverse data
• To employ analytical and numerical methods to mathematical problems

### Module syllabus

Descriptive statistics and elements of probability

Discrete random variables and probability distributions

Continuous random variables and probability distributions

Joint probability distributions and random samples

Parameter estimation and intervals

Hypothesis testing

Regression

### Pre-requisites

Mathematics I and II

Labs: 60 hours

### Assessments

Examinations:
●  Written exam: ; 100% weighting
Rubrics: One summer exam, 60 minutes, worth 100% (for credit).
No type of previous exam answers or solutions will be available