Module Artifacts — 10 items
An outline of the module's learning topics covering discrete probability distributions, PMFs, expected value, variance, and related distribution properties, used by learners and instructors to preview and navigate the module's scope.
A landing page for Module 4 that provides links to the lecture PowerPoint and recorded lecture video on discrete probability distributions, serving as a navigation hub for learners to access core instructional materials.
A comprehensive reference text covering random variables, PMFs, expected value, variance, and named discrete distributions (e.g., Binomial, Poisson, Geometric), used by learners as a study guide alongside the module lectures.
This reading introduces discrete probability distributions by explaining what a probability distribution is, why countable outcomes require discrete models, and how distributions form the foundation for quantifying uncertainty — learners read it to build conceptual grounding before studying specific distribution types.
This reading explains probability mass functions (PMFs), cumulative distribution functions (CDFs), and key properties such as non-negativity and summing to one, using examples like die rolls and coin flips — learners use it to understand the formal mathematical structure that all discrete distributions share.
This reading covers how to calculate and interpret expected value (mean) and variance for discrete random variables, including the formulas and their meaning as measures of center and spread — learners use it to summarize and compare distribution behavior quantitatively.
This reading explains the binomial distribution, its four required conditions (fixed trials, two outcomes, constant probability, independence), the PMF formula, and its mean and variance — learners use it to model and solve problems involving a fixed number of repeated binary-outcome experiments.
This reading introduces the Poisson distribution, explaining how it models the count of events occurring in a fixed interval of time, area, or volume, along with its PMF, single parameter λ, and mean and variance — learners use it to analyze rare or randomly occurring events when the binomial model does not apply.
This reading demonstrates how to identify which discrete distribution (binomial, Poisson, or other) applies to real-world engineering and applied-science scenarios and walks through problem-solving strategies for each — learners and instructors use it to practice selecting the correct model and executing full solutions on practical problems.
A group assignment in which students apply discrete probability distribution concepts to a semiconductor manufacturing quality-engineering scenario, requiring collaborative analysis and a written report submitted as a team.