Random Variables: AP Statistics: Free Course

About this course

Random variables connect outcomes with numerical values and probability distributions. This AP Statistics sequence examines expectation, variability, transformations and binomial and geometric models. Study the complete public source playlist from Khan Academy in English, with all 31 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Construct and validate discrete probability distributions.
• Interpret expected value, variance and standard deviation.
• Analyze transformations, sums and differences of random variables.
• Distinguish binomial from geometric probability models.

Skills you’ll gain

• Expected value
• Random variables
• Binomial models
• Geometric models

Course Overview

Discrete probability tables and continuous density curves provide two representations of a random variable. Mean and variance are then used to describe a distribution, with separate examples for scaling, shifting, sums and differences. Independence receives particular attention because it affects variance calculations even when expectations can still be combined. Binomial lessons model a fixed number of trials, while geometric lessons count trials up to a first success. Calculator demonstrations remain alongside formulas and proofs, including the expected value of a geometric variable. The sequence is the random-variables topic rather than a whole AP Statistics course, and original source order is retained.

How to study the course

• Videos 1–7: this part of the source list includes “Variance and standard deviation of a discrete random variable” through “Recognizing binomial variables”. Define the question and the observations. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 8–15: this part of the source list includes “Geometric random variables introduction” through “Constructing a probability distribution for random variable”. Check the assumptions behind a method. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 16–23: this part of the source list includes “Probability with discrete random variable example” through “Probability for a geometric random variable”. Connect a calculation with a plain-language interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 24–31: this part of the source list includes “Example: Transforming a discrete random variable” through “Binomial variables”. Describe uncertainty and limits of a conclusion. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits students, analysts and readers who want to understand the specific statistical methods in the course. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Basic arithmetic and familiarity with tables and graphs are helpful. More advanced probability or inference topics assume the prerequisite methods shown in the recordings.

Put the lessons into practice

Build a probability table for a small fictional game and calculate its expectation and variance. Then compare a fixed-trial success-count question with a first-success question. State the assumptions that justify each distribution. Apply a shift or scale to the game payouts and explain how the mean and standard deviation change.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.