Week 5/Module 4 - Discrete Probability Distributions — Topics & Learning Outcomes

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.

An introductory reading that defines discrete random variables and probability distributions, explaining how listing every possible value with its probability extends earlier work on single-event probability, which learners use to frame the rest of the module with engineering examples such as die rolls and counts of defective parts.

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.

A lesson on probability mass functions that covers how a PMF assigns probability to each value of a discrete random variable and the properties a valid distribution must satisfy (non-negative probabilities summing to one), with cumulative distribution ideas; learners use it to build and verify PMFs for counting scenarios like defective parts or packet drops.

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.

A reading on summarizing a distribution through expected value E(X) as the probability-weighted center and variance/standard deviation as the measure of spread, including the computational formulas; learners use it to calculate and interpret these summary measures for any discrete PMF.

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.

A topic covering the binomial distribution — the four conditions of fixed independent trials with constant success probability, the binomial PMF, and its mean and variance — which learners apply to problems such as counting defective parts in a sample of 50 or successful packet transmissions.

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.

A lesson on the Poisson distribution for modeling counts of events over a fixed interval of time, length, area, or volume using the rate parameter lambda, including its PMF, mean and variance, and its use as an approximation to the binomial; learners apply it to cases like weld defects per meter or help-desk calls per hour.

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 synthesis topic that teaches learners to read an unlabeled real-world scenario and choose among the Bernoulli, binomial, geometric, negative binomial, hypergeometric, and Poisson models, then carry out and interpret the calculation — useful as practice in model selection before assessments.