# 2022/23 Undergraduate Module Catalogue

## MATH2700 Probability and Statistics for Scientists

### 15 creditsClass Size: 50

Module manager: Dr Arief Gusnanto
Email: A.Gusnanto@leeds.ac.uk

Taught: Semesters 1 & 2 (Sep to Jun) View Timetable

Year running 2022/23

### This module is mutually exclusive with

 LUBS1240 Maths&Stats For Bus&Ec 1 MATH1710 Probability and Statistics I MATH1712 Probability and Statistics II

This module is not approved as a discovery module

### Module summary

This module introduces the fundamental ideas of probability and statistics that are essential for the rigorous application of scientific methods. The module provides a thorough introduction to the concepts of statistical theory and applications, including hypothesis testing, discrete and continuous random variables, statistical inference, exploratory data analysis, regression analysis, correlation, the calculation of confidence intervals, and the testing of independence.

### Objectives

The objective is to develop the knowledge and skills necessary to apply the foundational concepts of statistics and probability. Students will learn both the theoretical underpinnings of statistical techniques in tandem with direct hands-on application to scientific data in the assessed practicals.

Learning outcomes
On completion of this module, students should be able to:

(a) state and apply the fundamental rules of probability

(b) carry out exploratory data analysis, hypothesis testing and regression analysis

(c) understand discrete and continuous probability models

(d) understand the notions of prior and posterior probability

(e) understand the concepts of inference, carry out linear regression, and chi-squared tests

### Syllabus

1. Exploratory data analysis: numerical and graphical summaries.
2. Introduction to the axioms and rules of probability.
3. Joint and conditional probability. Independence and Bayes' formula.
4. Discrete random variables. The binomial distribution. Expectation and Variance.
5. Continuous random variables. Sampling distributions. The central limit theorem.
6. Models for data, and parameters. Prior and Posterior Distributions.
7. Point and interval estimation. Confidence intervals. Inference.
8. Hypothesis testing; the Z- and T-tests.
9. Several random variables. Covariance and correlation. Continuous bivariate distributions.
10. Regression. Binary data. Chi-squared tests. Fitting distributions. Goodness of fit tests. Contingency tables and tests of independence.

### Teaching methods

 Delivery type Number Length hours Student hours Tutorials 10 1.00 10.00 Lecture 44 1.00 44.00 Private study hours 96.00 Total Contact hours 54.00 Total hours (100hr per 10 credits) 150.00

### Private study

This will include study of the course material, working on the problem sets, preparation for workshops, using R for data analysis, and preparation for exams.

### Opportunities for Formative Feedback

Fortnightly workshops and coursework exercise sheets.

!!In order to pass the module, students must pass both examinations!!

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 30.00 Total percentage (Assessment Coursework) 30.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 35.00 Standard exam (closed essays, MCQs etc) 2 hr 00 mins 35.00 Total percentage (Assessment Exams) 70.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated