Week 6 — Readings & Resources · Random Variables

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective covered: Objective 4 — Work with random variables: distinguish discrete from continuous, read a probability distribution, and compute the expected value, variance, and standard deviation of a discrete random variable.

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.

This week's load is deliberately light: ~3 short readings + ~5 short videos, grouped by the four ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 45–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① discrete vs. continuous random variables → ② the probability distribution of a discrete RV → ③ expected value E(X) → ④ variance & standard deviation of a random variable.

A habit to start now: before you trust any computed answer below — or one a chatbot hands you — keep the week's checks in mind: Is the distribution valid (each P in [0, 1], and ΣP = 1)? Did the variance step subtract [E(X)]²?

① Discrete vs. Continuous Random Variables

Maps to Lecture Segment 2. The one test that settles it: are you counting or measuring? Count → discrete; measure on a ruler → continuous.

Reading — "What is the difference between discrete and continuous variables?" (Scribbr)
🔗 https://www.scribbr.com/frequently-asked-questions/discrete-vs-continuous-variables/
Why it's assigned: the cleanest one-screen version of the split we drew in class — discrete = counts, continuous = measurable amounts — with quick examples to test yourself on.
⏱ ~3 min

Reading — "Types of Variables in Research & Statistics" (Scribbr)
🔗 https://www.scribbr.com/methodology/types-of-variables/
Why it's assigned: puts discrete vs. continuous inside the bigger map of variable types you met earlier in the term, so the new vocabulary clicks into what you already know.
⏱ ~6 min

Video — "Random variables" (Khan Academy)
🔗 https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/random-variables
Why it earns the click: a 3-minute introduction to what a random variable is — chance attached to a number — exactly the idea that opens Segment 2.
⏱ ~3 min

Video — "Discrete and continuous random variables" (Khan Academy)
🔗 https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/discrete-and-continuous-random-variables
Why it earns the click: walks through several "count or measure?" judgment calls — including the ones that fool people (shoe size, time) — the same drill we ran in class.
⏱ ~9 min

② The Probability Distribution of a Discrete RV

Maps to Lecture Segment 3. The gatekeeper rule of the whole week: a distribution is valid only if every probability is between 0 and 1 and they add to exactly 1.

Reading — "Probability Distribution: Formula, Types, & Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/probability-distributions/
Why it's assigned: explains what a probability distribution is and shows discrete examples with a table of values and probabilities — the "complete map" of a random variable we built on the board.
⏱ ~7 min

Video — "Constructing a probability distribution for a random variable" (Khan Academy)
🔗 https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/discrete-probability-distribution
Why it earns the click: builds a discrete distribution from scratch (the number of heads in a few flips) and checks that the probabilities sum to 1 — a mirror of our two-coin-flip example.
⏱ ~7 min

③ Expected Value E(X)

Maps to Lecture Segment 4. The line to carry: expected value is each outcome times its chance, all added up — a long-run average, not the next outcome. (A fair die's E(X) is 3.5, which you can never roll.)

Video — "Mean (expected value) of a discrete random variable" (Khan Academy)
🔗 https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/expected-value-of-a-discrete-random-variable
Why it earns the click: computes E(X) as the probability-weighted average, step by step — the exact "multiply each value by its probability, then add" move from Segment 4.
⏱ ~7 min

④ Variance & Standard Deviation of a Random Variable

Maps to Lecture Segment 5. Remember the recipe: mean of the squares minus the square of the mean, then take the square root to get back to real units. The classic slip is forgetting to subtract [E(X)]².

Video — "Variance and standard deviation of a discrete random variable" (Khan Academy)
🔗 https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/variance-and-standard-deviation-of-a-discrete-random-variable
Why it earns the click: works the spread of a discrete random variable end to end — the squared distances, the probability weighting, and the square root — so the variance-and-SD steps from class stick.
⏱ ~10 min

Video — "The Shape of Data: Distributions — Crash Course Statistics #7"
🔗 https://www.youtube.com/watch?v=bPFNxD3Yg6U
Why it earns the click: the liveliest big-picture tour of distributions — what a probability distribution describes and how its center and spread summarize a random outcome — a fun companion to the week's machinery.
⏱ ~12 min

Optional one-stop reference (free online text)

If you'd like one optional reference to skim all term, OpenIntro Statistics keeps its full text and per-section videos free to read online. Chapter 3 ("Probability") covers this week directly: Section 3.4 ("Random variables") is exactly our material — discrete distributions, expected value, and variance — and Section 3.5 ("Continuous distributions") previews where continuous random variables go next.
🔗 https://www.openintro.org/book/os/
Why it's here: a reputable, currently-available reference you can return to in later weeks — entirely optional this week.

Pick-one quick path (≈15 min total)

In a hurry? Do exactly these four and you'll be ready for the quiz:
1. Read Discrete vs. Continuous Variables (group ①).
2. Watch Constructing a probability distribution (group ②).
3. Watch Mean (expected value) of a discrete random variable (group ③).
4. Watch Variance and standard deviation of a discrete random variable (group ④).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Rivera and use the OpenIntro reference above (Chapter 3) in the meantime.