Probability and Statistics

(3-4 Credit Hours) · Undergraduate

Taught at a host institution. STAT 20060 at UCD; This module introduces the basic concepts of statistical modelling, which particular emphasis on engineeringapplications.Strong emphasis is placed on using the material covered in problem-solvingscenarios.The main sections of the course are:1) Descriptive StatisticsMean, median, mode, range, standard deviation, interquartile range, percentiles.2) Graphical MethodsPie charts, bar graphs, histograms, stem-and-leaf plots, cumulative frequencycurves, Venn diagrams.3) Laws of ProbabilityLaw of total probability, additive rule, multiplicative rule, mutually exclusive events,dependent and independent events, conditional probability, combinations rule,permutations rule, mean and variance of functions of random variables.4) Discrete DistributionsDiscrete random variables, E(X) and Var(X) for X discrete, binomial distribution,poisson distribution, hypergeometric distribution.5) Continuous DistributionsContinuous random variables, density functions, cumulative density functions, E(X)and Var(X) for X continuous, uniform distribution, exponential distribution, normaldistribution, Z values, standard normal distribution, Student's t-distribution.6) Confidence Intervals and Hypothesis TestingSampling distributions, biased and unbiased estimators, significance level, CentralLimit Theorem, large sample confidence interval for a population mean, small sampleconfidence interval for a population mean, large sample confidence interval for apopulation proportion, sample size calculations.7) RegressionCorrelation coefficient, residuals, simple linear regression, correlation and causation,coefficient of determination, making predictions from the regression equation.In addition students are required to complete a sequence of computer laboratorysessions using an interactive package that allows them to simulate commonprobability problems; and use Microsoft Excel to analyse data and perform regressionanalysis. Also taken in Heidelberg. National University of Singapore: This course introduces students to basic probability theory and statistical inference. Topics include basic concepts of probability, conditional probability, independence, random variables, joint and marginal distributions, mean and variance, some common probability distributions, sampling distributions, estimation and hypothesis testing based on a normal population. Students will learn basic probability theory and statistics. Including conditional probability, random variables, mean and variance, and more. Sydney, Australia (SY): https://www.sydney.edu.au/units/STAT2011/2026-S1C-ND-CC This unit offers a foundational introduction to probability theory and statistical inference, focusing on key concepts such as random variables and widely used probability distributions¿including the Binomial, Hypergeometric, Poisson, Normal, Geometric, and Gamma distributions. Students will engage with univariate data analysis techniques and gain practical skills in modelling variability using real-world data. Core estimation methods, including the method of moments, maximum likelihood estimation, and associated inference procedures are introduced in a rigorous yet accessible manner. Weekly computer laboratory sessions provide hands-on experience with statistical software for simulation, distribution fitting, and computational methods such as the bootstrap. By the end of the unit, students will have developed essential statistical modelling competencies, equipping them for further study in advanced statistical analysis and data science. PA - Perth, Australia (SC & EG): Many real-world problems involve analysing data sets that are not normally distributed. For example, binomial data in the form of presence/absence recordings, Poisson data measured as counts of rare events such as car accidents, Gamma data for measurements of rainfall and Weibull data for the expected lifetimes of machinery. This unit provides experience in analysing such observations. The majority of the unit concentrates on the presentation and analysis of such data sets. Generalised Linear Models (GLMs) are used to incorporate explanatory variables into the analyses. In developing these skills students are trained in an appropriate statistical software package. The unit also provides a rudimentary understanding of probability and statistics necessary for applying the likelihood theory for estimating these models.