Week 6 — Readings & Resources · Random Variables
Course: Introduction to Statistics (18-week generic edition)
Objective covered: Objective 4 — probability rules and random variables (this week: the random-variables half).
Your primary reading is Chapter 6 (in this module). Everything below is the optional, go-deeper layer.
How to use this page
Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded, and nothing costs money.
The load is deliberately light: 4 short readings + 5 short videos, grouped by the four big ideas of the week. Read or watch one item per group and you're well prepared; do all of them and you'll be very comfortable. Total time is roughly 60–70 minutes if you do everything, far less if you pick one per group.
Order that matches the chapter and lecture: ① what a random variable is & its distribution → ② expected value → ③ variance, SD & transformations → ④ continuous variables & density curves.
A habit for this week: every time a source shows you a distribution table, run the two legitimacy rules yourself before reading on — is every probability between 0 and 1, and do they total exactly 1?
① What a Random Variable Is · Discrete Distributions
Maps to Chapter 6, Sections 1–2 and Lecture Segments 2. The hook to carry in: discrete you count, continuous you measure — and a discrete variable's whole personality lives in one values-and-probabilities table.
Reading — Probability Distribution: Formula, Types, & Examples (Scribbr)
🔗 https://www.scribbr.com/statistics/probability-distributions/
Why it's assigned: the cleanest plain-language tour of what a distribution is, with the discrete/continuous split and expected value handled in the same friendly voice as our chapter.
⏱ ~12 min (read the sections through "expected value"; the named distributions near the end are later weeks' material)
Video — An Introduction to Discrete Random Variables and Discrete Probability Distributions (jbstatistics) (video, ~9 min, captioned)
🔗 https://www.youtube.com/watch?v=oHcrna8Fk18
Why it earns the click: builds the values-and-probabilities table from scratch and reads probabilities out of it — exactly this week's Segment 2, at a whiteboard.
Video — Random variables | Probability and Statistics (Khan Academy) (video, ~10 min, captioned)
🔗 https://www.youtube.com/watch?v=3v9w79NhsfI
Why it earns the click: the gentlest possible on-ramp to the "a number chance hasn't decided yet" idea and the capital-X notation.
② Expected Value: What a Chance Is Worth
Maps to Chapter 6, Section 3 and Lecture Segment 3. The line that survives the term: expected value is what you'd average, not what you'd expect.
Reading — 4.2 Mean or Expected Value and Standard Deviation (OpenStax Introductory Statistics 2e)
🔗 https://openstax.org/books/introductory-statistics-2e/pages/4-2-mean-or-expected-value-and-standard-deviation
Why it's assigned: the "long-term average" framing matches ours exactly, and its worked examples (including a lottery-style loss) are perfect parallel practice for the claw-machine computation.
⏱ ~12 min
Video — Expected Values, Main Ideas!!! (StatQuest with Josh Starmer) (video, ~13 min, captioned)
🔗 https://www.youtube.com/watch?v=KLs_7b7SKi4
Why it earns the click: the most intuition-first explanation on the internet of why we weight by probability — and of what the resulting number does and doesn't promise you.
③ Variance, SD & Linear Transformations
Maps to Chapter 6, Sections 4–5 and Lecture Segments 5–6. Remember the two hooks: variance is scratch work, the SD is the answer you say out loud — and adding shifts the center; multiplying stretches both.
Reading — Random Variables: Mean, Variance and Standard Deviation (Math is Fun)
🔗 https://www.mathsisfun.com/data/random-variables-mean-variance.html
Why it's assigned: short, concrete, and generous with worked tables; it also shows an equivalent "shortcut" variance formula (Σx²p − μ²) — same answer as our deviations method, so use whichever your brain likes, but show your steps either way.
⏱ ~10 min
Video — The Expected Value and Variance of Discrete Random Variables (jbstatistics) (video, ~10 min, captioned)
🔗 https://www.youtube.com/watch?v=Vyk8HQOckIE
Why it earns the click: works one distribution all the way from E(X) through the weighted squared deviations to the SD — the exact grind from our vehicles-per-household example, narrated.
④ Continuous Random Variables · Probability as Area
Maps to Chapter 6, Section 6 and Lecture Segment 7. The trade to internalize: for continuous variables the table is replaced by a density curve, probability becomes area, and any single exact value has probability zero.
Reading — 5.1 Continuous Probability Functions (OpenStax Introductory Statistics 2e)
🔗 https://openstax.org/books/introductory-statistics-2e/pages/5-1-continuous-probability-functions
Why it's assigned: states the week's punchline in flashing lights — "for continuous probability distributions, PROBABILITY = AREA" — and computes rectangle areas for a uniform density, just like our clock-face example.
⏱ ~10 min
Video — An Introduction to Continuous Probability Distributions (jbstatistics) (video, ~6 min, captioned)
🔗 https://www.youtube.com/watch?v=OWSOhpS00_s
Why it earns the click: six tight minutes on density curves, area-as-probability, and why P(X = a) = 0 — the whole of Segment 7 in video form.
Optional one-stop reference (free online text)
If you'd like one optional reference to skim all term, OpenStax Introductory Statistics 2e keeps its full text free to read online. Chapter 4 (Discrete Random Variables) covers this week's tables, expected values, and SDs end to end — and its Section 5.1 (linked above) opens the continuous story.
🔗 https://openstax.org/books/introductory-statistics-2e/pages/4-introduction
Why it's here: a reputable, currently-available reference you can return to in later weeks — entirely optional this week. (Skip its binomial/Poisson sections for now; the binomial is next week's star, and Poisson isn't in our course.)
Pick-one quick path (≈25 min total)
In a hurry? You've read Chapter 6 — then do exactly these three and you'll be ready for the quiz:
1. Watch jbstatistics — Discrete Random Variables (group ①).
2. Watch StatQuest — Expected Values (group ②).
3. Read OpenStax 5.1 — Continuous Probability Functions (group ④).
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 OpenStax reference above in the meantime.