This rubric outlines the key learning objectives and expectations for an Undergraduate Year 3 (Junior) Probability & Statistics course. Students will develop a strong theoretical and applied understanding of probability distributions; statistical inference; and data analysis techniques. The course emphasizes critical thinking and problem-solving skills; enabling students to interpret real-world data with precision and confidence. Students will master foundational probability concepts; including discrete and continuous random variables; expectation; variance; and moment-generating functions. They will apply these principles to model uncertainty in various contexts. The curriculum also covers key statistical methods such as point and interval estimation; hypothesis testing; and regression analysis. Through hands-on exercises; students will learn to select appropriate statistical tools; justify their choices; and communicate results effectively. A major focus is on understanding the assumptions and limitations of statistical models. Students will evaluate the validity of inferences by assessing conditions like independence; normality; and sample size. They will also explore advanced topics such as maximum likelihood estimation; Bayesian inference; and nonparametric methods; gaining exposure to modern statistical approaches. Collaborative projects and case studies will reinforce practical skills in data analysis using statistical software. By working with real datasets; students will develop the ability to clean; visualize; and interpret data while adhering to ethical guidelines. The course prepares students for advanced coursework; research; and professional applications in fields such as data science; economics; and engineering. Successful completion ensures students can rigorously analyze probabilistic systems; draw meaningful conclusions from data; and present findings with clarity and accuracy. These competencies are essential for academic and career success in quantitative disciplines.
