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Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title Probability, Descriptive & Inferential Statis
Module Code MS263 (ITS) / MTH1048 (Banner)
Faculty Science & Health School Mathematical Sciences
Module Co-ordinatorMingchuan Zhao
Module Teachers-
NFQ level 8 Credit Rating 7.5
Pre-requisite Not Available
Co-requisite Not Available
Compatibles Not Available
Incompatibles Not Available
None
Description

The aim of this module is to give a thorough grounding in probability, descriptive and inferential statistics, with an emphasis on the acquisition of both skills and understanding. Students will learn how probability and statistics can be used as a tool for solving problems and as a language for communicating information. Students will participate in the following learning activities: a) Lectures which are designed to introduce learners to the mathematical principles and problem solving techniques that underpin this module. b) Tutorials for which problem sheets based on lecture content will be distributed for the students to attempt in advance. c) Reading the textbooks recommended.

Learning Outcomes

1. Apply the rules of probability, assign probabilities to events, obtain expectations of discrete and continuous random variables.
2. Test statistical hypotheses and compute confidence intervals.
3. Demonstrate an understanding of concepts by use of examples or counterexamples.
4. Discuss the assumptions and limitations of conclusions drawn from sample data or graphical/numerical summaries of data



Workload Full-time hours per semester
Type Hours Description
Lecture36No Description
Tutorial12No Description
Independent Study109No Description
Directed learning30No Description
Total Workload: 187

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Sets
Definitions, set operations; set identities. Russell's paradox.

Organising and Describing Data
Measures of central tendency and variability; graphical summaries.

Probability
Random experiments; axioms of probability; independent events; conditional probability; Bayes' theorem

Random Variables
Discrete and continuous random variables; characteristics of random variables; probability distributions and densities.

Probability Density Functions
Basic combinatorics, the binomial, Poisson, Pascal and normal distributions.

Sampling
Random samples; sampling distribution; the central limit theorem; point estimation.

Hypothesis Testing
Confidence intervals; hypothesis tests.

Simple Linear Regression
Least squares; regression model; correlation.

Assessment Breakdown
Continuous Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class Testn/a10%As required
Assignmentn/a10%As required
Reassessment Requirement Type
Resit arrangements are explained by the following categories:
Resit category 1: A resit is available for both* components of the module.
Resit category 2: No resit is available for a 100% continuous assessment module.
Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3
Indicative Reading List

  • J.J. Kinney: 2002, Statistics for Science and Engineering, AddisonWesley,
  • J. I. Barragués, A. Morais and J.Guisasola: 2014, Probability and Statistics : A Didactic Introduction, Taylor and Francis,
Other Resources

None

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