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Introduction to Probability & Statistics - MAT00004C

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  • Department: Mathematics
  • Module co-ordinator: Dr. Stephen Connor
  • Credit value: 20 credits
  • Credit level: C
  • Academic year of delivery: 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

Pre-requisite modules

  • None

Co-requisite modules

Prohibited combinations

  • None

Additional information

Post-requisite modules:
Statistics stream

 

Module will run

Occurrence Teaching period
A Semester 1 2023-24

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, available in Stage 2

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)

Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam: Introduction to Probability & Statistics		 2 hours 70
Coursework - extensions not feasible/practicable
Coursework		 N/A 10
Essay/coursework
Introduction to Probability and Statistics - Computational Exercises		 N/A 20

Special assessment rules

None

Additional assessment information

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

NB the 10% “written solution” element of the coursework is merged with the exam, so if a student fails the module they resit the exam for 80%. If they have passed the 20% computer-based coursework they may keep that mark, or they may choose to resit it.

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).

For extreme exceptional circumstances cases, the 10% coursework component can be discounted, with the exam mark making up 80% of the module

Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Introduction to Probability & Statistics		 2 hours 80
Essay/coursework
Coursework - Computational exercises		 N/A 20

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.


The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.