Probability and Statistics / Data Analysis / Python
Probability and Statistics Jigsaw Puzzle: Probability Calculations and Chi-Square Analysis in Python
This technical Probability and Statistics exercise presents a set of Python code fragments designed to demonstrate basic probability calculations and statistical hypothesis testing. The material is organised as a jigsaw-style collection of code segments, allowing the underlying logical sequence to be reconstructed from variable definitions, probability calculations, observed data, statistical testing and final interpretation. Jigsaw_Puzzle_3_Original_Struct… The first part models a two-bag probability problem. Bag 1 contains four white and two black items, while Bag 2 contains three white and five black items. The code calculates the probabilities of selecting a white or black item from each bag and then uses multiplication rules to determine the probability of drawing two white items, two black items, or one white and one black item across the two bags. Jigsaw_Puzzle_3_Original_Struct… Jigsaw_Puzzle_3_Original_Struct… Jigsaw_Puzzle_3_Original_Struct… A second section demonstrates a chi-square test of independence using an observed frequency table containing grade outcomes for girls and boys across grades A, B, C and D. The data are stored in a NumPy array and analysed using SciPy's chi2_contingency function. The resulting chi-square statistic, p-value, degrees of freedom and expected frequencies are calculated and displayed. Jigsaw_Puzzle_3_Original_Struct… Jigsaw_Puzzle_3_Original_Struct… The final fragment applies a conventional significance threshold of α = 0.05. If the p-value is greater than 0.05, the code reports that the null hypothesis should not be rejected; otherwise, it concludes that a statistically significant difference exists. Jigsaw_Puzzle_3_Original_Struct… Overall, the document demonstrates core statistical-programming concepts including probability rules, contingency tables, chi-square analysis, expected frequencies, p-value interpretation and hypothesis testing using Python, NumPy and SciPy. Important: because this file does not identify a university, module, academic level, academic year, assignment brief, formal word count or referencing system, I would leave those fields as Not specified rather than guessing.
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Statistical Programming / Data Science / Business Analytics
Statistical Programming with R: Data Analysis, Probability, Regression and Business Decision-Making
This Statistical Programming assessment evaluates students' ability to apply statistical techniques and R programming to practical data-science and business decision-making problems. The individual assessment combines descriptive statistics, data preparation, visualisation, probability, regression, correlation and sampling, requiring students to demonstrate both conceptual statistical understanding and practical implementation in RStudio. The module learning outcomes emphasise the application of statistical methods to large and real-world datasets, critical evaluation of analytical techniques and awareness of legal, cultural and ethical issues associated with data analysis and dissemination. KL7012 - Statistical Programmin… The early tasks examine fundamental statistical reasoning. Students interpret weight-loss data comparing exercise classes with gym-only workouts using sample size, mean, mode and standard deviation, and explain an appropriate method for dealing with missing data, including its advantages and disadvantages. KL7012 - Statistical Programmin… A substantial practical component uses a cystic fibrosis dataset containing variables such as age, sex, height, weight, body-mass-related measurements, forced expiratory volume, residual volume, functional residual capacity, total lung capacity and maximum expiratory pressure. Students import the data into an R data frame, generate descriptive summaries and interpret the results. They then use scatterplots to investigate relationships between variables and sex-stratified boxplots to identify possible outliers. KL7012 - Statistical Programmin… The assessment also covers major probability models. Students apply probability concepts to healthcare survival, helpdesk email arrivals and fuel-demand scenarios, while also discussing how changing assumptions or real-world conditions can affect interpretation. These exercises assess understanding of statistical distributions and their application to operational and managerial decision-making. KL7012 - Statistical Programmin… Further analytical tasks examine linear regression and correlation. Students analyse the relationship between temperature and converted sugar in a chemical process, use a regression model to estimate the expected response at a specified temperature, and interpret relevant summary statistics. They also calculate and evaluate the suitability of a correlation coefficient for examining the relationship between advertising activity and product purchases. KL7012 - Statistical Programmin… The final and most substantial task involves a real-world M1 traffic-speed investigation for a manufacturing organisation. Students must design an appropriate sampling strategy, collect data from the specified Traffic England source, conduct statistical analysis in RStudio and develop evidence-based conclusions. The statistical report for this task is limited to 1,500 words and should include sampling methodology, collected data, statistical analysis, results, conclusions and relevant background research, supported by appropriate graphs, tables and charts. Raw data and RStudio calculations must be included in an appendix. KL7012 - Statistical Programmin… Overall, the assessment integrates statistical theory with R-based practical analysis, covering descriptive statistics, probability, visualisation, missing-data treatment, regression, correlation, sampling and critical interpretation of results in healthcare, operational and business contexts.
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Computer Science / Algorithms and Optimisation
Genetic Algorithms for the Balanced Spanning Tree Problem
This technical research work investigates the Balanced Spanning Tree Problem, an optimisation problem that seeks to construct a spanning tree capable of balancing two competing network objectives: the low overall cost associated with a Minimum Spanning Tree and the short source-to-destination distances provided by a Shortest Path Tree. For an undirected, weighted and connected graph with a designated root vertex, a balanced spanning tree is defined using two parameters, α and β. The first limits the distance between the root and each vertex relative to the corresponding shortest path in the original graph, while the second limits the total tree weight relative to the Minimum Spanning Tree. Finding an optimal balanced spanning tree is computationally challenging because determining whether a graph contains an (α, β)-balanced spanning tree is an NP-complete problem. The research therefore proposes genetic algorithms as heuristic optimisation techniques for two variants of the problem: minimising β while α is fixed, and minimising α while β is fixed. The proposed genetic algorithm represents individual spanning trees as chromosomes composed of graph edges. An initial population of valid spanning trees is generated before evolutionary operations are repeatedly applied. The approach incorporates chromosome selection, crossover, mutation, fitness evaluation and stopping criteria. Four selection strategies are examined: Random Selection, Roulette Wheel Selection, Stochastic Universal Sampling and Tournament Selection. The fitness function is based on the relationship between the Minimum Spanning Tree weight and the total weight of the candidate chromosome. Experimental evaluation is performed using randomly generated weighted graphs containing 6, 10, 15 and 20 vertices. The experiments investigate different values of the balancing parameters, selection mechanisms and population sizes. The implementation uses a population size of 30, a maximum of 300 generations, crossover probability of 0.9 and mutation probability of 0.01 in the principal experiments. The reported results show that the genetic approach can generate high-quality balanced spanning trees and, for the tested instances, produced solutions matching the corresponding optimal balanced spanning trees. The study also examines how balancing parameters and population size influence execution time and convergence, demonstrating the practical use of evolutionary computation for complex graph-optimisation problems.
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