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Module Code - Title:

MA4704 - TECHNOLOGICAL MATHEMATICS 4

Year Last Offered:

2022/3

Hours Per Week:

Lecture

3

Lab

0

Tutorial

1

Other

0

Private

6

Credits

6

Grading Type:

N

Prerequisite Modules:

MA4702
MA4701

Rationale and Purpose of the Module:

To introduce students to the fundamental ideas of uncertainty through probability. To lay a good foundation for the stream of statistically oriented modules in the fourth year. To introduce students to the most widely used statistical distributions and applications thereof. To introduce statistical inference through the concepts of estimation and hypothesis testing.

Syllabus:

[Variables] - continuous and discrete. [Representation of variables] - frequency tables, histograms, bar charts, etc. [Reduction of variables] - measures of location and dispersion, mean, variance, range, median, quartiles, etc. [Introduction to the fundamentals of probability]. Experiments, sample spaces, events. Laws of probability - addition and multiplication, conditional probability. [Bayes theorem], prior and posterior distributions. [Introduction to random variables], probability density functions. [Special distributions] [binomial, Poisson, geometric, uniform, exponential, normal]. [Statistical inference], point and interval estimates, standard error of an estimator, hypothesis testing, one and two-tailed tests. One and two sample problems for the mean, variance and proportion. [Non-parametric tests] - sign test, rank tests. [Correlation and Regression] - method of least squares.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

Explain continuous and discrete variables. Represent variables - frequency tables, histograms, bar charts, etc. Understand mean, variance, range, median, quartiles, etc. Introduce the fundamentals of probability. Apply Bayes theorem and understand prior and posterior distributions. Use probability density functions. Analyse Statistical inference using point and interval estimates Understand one and two sample problems for the mean, variance and proportion. An overview of non-parametric tests Introduce Correlation and Regression

Affective (Attitudes and Values)

N/A

Psychomotor (Physical Skills)

N/A

How the Module will be Taught and what will be the Learning Experiences of the Students:

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

Utts, J.M. and Heckard, R.J. (2012) Mind on Statistics , Cengage Learning

Other Relevant Texts:

Field, A. (2013) Discovering Statistics Using IBM SPSS Statistics , SAGE

Programme(s) in which this Module is Offered:

Semester - Year to be First Offered:

Spring - 08/09

Module Leader:

david.osullivan@ul.ie