Module Specifications.
Current Academic Year 2024 - 2025
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Date posted: September 2024
No Banner module data is available
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Repeat examination |
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Description 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. | |||||||||||||||||||||||||||||||||||||||||
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 |
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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. Estimation 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. | |||||||||||||||||||||||||||||||||||||||||
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||