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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Statistics I
Module Code MS226
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Vladimir Krylov
Semester 2: Vladimir Krylov
Autumn: Vladimir Krylov
Module TeachersVladimir Krylov
NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
Repeat examination

MS226 aims to provide students with an introduction to the basics of statistics, including the use of common discrete and continuous distributions, central limit theorem, sampling techniques as well as estimation and hypothesis testing techniques. Practical examples will be provided throughout using R.

Learning Outcomes

1. Define and apply common discrete and continuous distributions. Extend the theory to joint distributions and conditional distributions.
2. State the Central Limit Theorem. Define a random sample and sampling distributions. Apply basic statistical tests to random samples from a Normal distribution.
3. Estimate parameters using the method of moments and maximum likelihood estimation. Understand the properties of estimators.
4. Perform basic hypothesis tests and tests for goodness of fit.
5. Calculate confidence intervals for common distributions.

Workload Full-time hours per semester
Type Hours Description
Laboratory10Computer labs
Independent Study138Individual
Total Workload: 188

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

Probability Distributions
Discrete: Uniform, binomial, Poisson, geometric, negative binomial, hypergeometric. Continuous: Uniform, normal, log normal, exponential, gamma, chi-square, t, F, beta. Application of distributions using R. Use of generating functions to determine the moments and cumulants of random variables.

Joint Distributions and Conditional Distributions
Explain joint distributions, marginal distributions and conditional distributions. Calculate the expected value, correlation and covariance of jointly distributed random variables. Extend to linear combinations of random variables. Calculate conditional expectations.

Sampling Distributions
State the Central Limit Theorem and understand its fundamental importance in statistics. Understand the use of samples in statistical inference for a population. Define the sampling distributions for the sample mean (normal and t distributions) and sample variance. Ratio of sample variances from Normal distributions and the F-statistic.

Use of method of moments and MLE for parameter estimation. Consideration and use of efficiency, consistency, bias, mean square error, asymptotic distribution of MLEs. Bootstrapping and the use of empirical distributions. Implementation of methods using R.

Confidence Intervals
Define confidence intervals for common distributions. Calculate confidence intervals for two sample situations and paired data. Calculation of confidence intervals in R.

Hypothesis testing
Theory – null and alternative hypothesis, error types, LRT, level of significance. Critical value approach and probability value approach. Application of hypothesis testing for one and two sample situations for common distributions. Goodness of fit test. Contingency tables. Use of R to perform hypothesis tests and interpretation of R output.

Assessment Breakdown
Continuous Assessment30% Examination Weight70%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Assignmentlab assignment30%n/a
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
This module is category 1
Indicative Reading List

    Other Resources

    Programme or List of Programmes
    ACMBSc in Actuarial Mathematics
    BPMBSc in Psychology with Mathematics
    BSSAStudy Abroad (DCU Business School)
    CAFMCommon Entry, Actuarial, Financial Maths
    DSBSc in Data Science

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