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Introduction to Probability & Statistics - MAT00004C

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• Department: Mathematics
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2024-25
  • See module specification for other years: 2022-23 2023-24

Module summary

This module: introduces the basic concepts of probability theory and statistics, illustrated by a full range of examples and applications; introduces an important statistical computing package (R); provides secure and solid foundations for higher level probability and mathematical statistics modules.

Related modules

Additional information

Post-requisite modules:
Statistics stream

 

Module will run

Occurrence	Teaching period
A	Semester 1 2024-25

Module aims

This module: introduces the basic concepts of probability theory and statistics, illustrated by a full range of examples and applications; introduces an important statistical computing package (R); provides secure and solid foundations for higher level probability and mathematical statistics modules.

Module learning outcomes

By the end of the module, students will be able to:

1. model simple experiments using probability theory;

2. perform standard probability calculations;

3. work with independent and correlated random variables;

4. correctly apply simple formal statistical techniques and interpret the results;

5. carry out introductory data analysis and simulations using a statistical computing package

Module content

Axioms of probability

Independence

Bayes Theorem

Random variables and moments

Joint distributions (mainly discrete) and covariance

LLN and CLT

Statistical models

Estimators (including what it means to be unbiased)

Confidence intervals for mean of a normal distribution (variance known/unknown)

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	70
Coursework - extensions not feasible/practicable	30

Special assessment rules

None

Additional assessment information

If a student has a failing module mark, only failed components need be reassessed.

Note:

Due to the pedagogical desire to provide speedy feedback in seminars, extensions to the written coursework and computer exercises are not possible. (This is the current practice in this module).

To mitigate for exceptional circumstances, the written coursework grade will be the best 4 out of the 5 assignments. If more than one assignment is affected by exceptional circumstances, an ECA claim must be submitted (with evidence).

Similarly, the computational grade will be the best 4 out of the 5 exercises. If more than one exercise is affected by exceptional circumstances, an ECA claim must be submitted (with evidence).

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	70
Coursework - extensions not feasible/practicable	30

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

This module follows a set textbook:

A Modern Introduction to Probability and Statistics, Understanding Why and How by F.M. Dekking et.al., Springer 2005.