Week 6 — Readings & Resources

Your primary reading is Chapter 6 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 11 items (5 readings and 6 videos). Allow 113–137 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (18–25 min total)

• Variance & Standard Deviation of a Discrete Random Variable — Radford Mathematics
• Random Variables - Mean, Variance, Standard Deviation — Math is Fun

① What makes a number random? Random variables and their distributions

Chapter 6, Section “Probability distributions: check that the table is legitimate” · Session 1, Segment 1, “Random variables and probability distributions” · Remember: a probability distribution lists every value with its chance, each chance sits between 0 and 1, and the chances add to exactly 1.

• An Introduction to Discrete Random Variables and Discrete Probability Distributions — jbstatistics — a careful walk through telling discrete random variables from continuous ones, then building a probability table and checking the two rules it must follow. This builds on Week 5's work with the basic rules of probability. (video, 14 min) (captions: automatic)
• Seeing Theory - Probability Distributions — Seeing Theory — interactive charts where you build your own random variable and compare discrete and continuous distributions; read the Random Variables and Discrete and Continuous parts. Stop here before the binomial and normal shapes in the dropdown menu and the Central Limit Theorem part; next week takes up the binomial and normal models. (reading, 10–15 min)

② What is it worth on average? Expected value

Chapter 6, Section “Expected value: the long-run average, not the next result” · Session 1, Segment 2, “Expected value” · Remember: an expected value is the average over many tries, and it need not be a value you can actually get.

• Expected Values, Main Ideas!!! — StatQuest with Josh Starmer — two worked examples that build the expected value as a long-run average, with the summation notation explained one step at a time; it opens with a short song. (video, 14 min) (captions: automatic)
• Randomness: Crash Course Statistics #17 — CrashCourse — a brisk simulation of what the expected value and the variance tell you about something random; watch the first seven minutes and skip the parts on skewness and on combining random variables. (video, 12 min) (captions: creator)
• Random Variables - Mean, Variance, Standard Deviation — Math is Fun — a gentle page with a weighted-die example and a small-business profit example, each worked from the probability table to the mean, the variance, and the standard deviation; use it while completing the Week-6 module overview. (reading, 8–15 min)

③ How far does one result wander? Spread, shifting, and rescaling

Chapter 6, Section “Variance and standard deviation: measure how far results typically land” · Session 2, Segment 3, “Variance, standard deviation, shifting, and rescaling” · Remember: square each distance from the mean, weight it by its chance, add, and take the square root; a shift moves the mean, and a rescale stretches both.

• Variance & Standard Deviation of a Discrete Random Variable — Radford Mathematics — one worked example that computes the variance from a probability table and then takes the square root to reach the standard deviation; pause before each step and try it first. (video, 10 min) (captions: automatic)
• AP Statistics | 6.2.1 | Linear Transformations of Random Variables — Mostly Math with Ashley — a worked example showing that adding a constant moves the mean but not the spread, while multiplying by a constant scales both. (video, 15 min) (captions: automatic)
• Linear Transformation — Stat Trek — the rules for what adding or multiplying by a constant does to a random variable's mean, variance, and standard deviation, with two practice problems to try; this course multiplies only by positive constants. (reading, 8–12 min)

④ What if any value is possible? Density curves

Chapter 6, Section “Density curves: probability becomes area” · Session 2, Segment 4, “Density curves” · Remember: for a continuous random variable, probability is area under the curve, and a single exact value has probability 0.

• An Introduction to Continuous Probability Distributions — jbstatistics — a short introduction to density curves: probability is area, the total area is 1, and a single exact value has probability 0; stop at about the four-minute mark, before the parts on common distributions and integration. (video, 6 min) (captions: creator)
• Random Variables - Continuous — Math is Fun — the plain-language page on continuous random variables and why probability becomes area; read the opening sections and skip the cumulative-distribution and normal-table parts. (reading, 8–12 min)

Optional one-stop reference (free online reference)

• 1.3.6.1. What is a Probability Distribution — NIST/SEMATECH e-Handbook of Statistical Methods — a free government reference section on discrete and continuous probability distributions; read the plain-language explanations of probabilities that add to 1 and of probability as area, and skip the integral formulas. (reading, 8–12 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

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