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ap statistics - transforming & combining random variables

originally streamed in 2019 with Shane DurkanTeacher
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Learn how to transform and combine random variables for AP Statistics. This review covers expected value, variance, and standard deviation rules you need for the AP exam. We'll walk through discrete vs continuous variables, transforming random varia ...more

covered in this stream

units
Unit 4 – Probability, Random Variables, and Probability Distributions
topics
4.7 Introduction to Random Variables and Probability Distributions4.8 Mean and Standard Deviation of Random Variables4.9 Combining Random Variables

timestamps

  • 0:00

    Introduction and Session Overview

  • 0:35

    Weekly Schedule and Agenda

  • 1:37

    Discrete vs Continuous Variables

  • 2:40

    Discrete Variable Explanation

  • 3:12

    Puppies Litter Example

  • 4:45

    Continuous Variables Overview

  • 5:16

    Transforming Random Variables

  • 5:47

    Vet Fees Transformation Example

  • 7:51

    Calculator Expected Value Demo

  • 10:28

    Multiplying Transformation Process

  • 12:36

    Rule for Multiplying/Dividing

  • 14:11

    Adding Transformation Example

  • 15:46

    Calculator Adding Demo

  • 17:23

    Rule for Adding/Subtracting

  • 18:26

    Combining Random Variables

  • 19:27

    Variance for Combining Variables

  • 22:32

    Transition to Examples

  • 23:36

    Casino Game Example

  • 26:46

    Total Amount Calculation

  • 30:33

    Contestant Gain Analysis

  • 32:36

    Closing and Q&A

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© 2026 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

every AP exam is fiveable

Fiveable

Study Content & Tools

Study GuidesFRQs + AI ScoringAP Essay Grader for StudentsAI Grading for TeachersPractice QuestionsGlossaryScore Calculators

Company

What's New?PricingBulk DiscountsTestimonialsFAQsEmail us

Resources

AP Exam Schedule 2027AP Exam AccommodationsAP ClassesAP ClassroomEasiest AP ClassesHardest AP ClassesAP vs IBAP vs Dual EnrollmentAP vs Honors ClassesAP Scholar Awards

history

🌎 ap world history🇺🇸 ap us history🇪🇺 ap european history

social science

✊🏿 ap african american studies🗳️ ap comparative government🚜 ap human geography💶 ap macroeconomics🤑 ap microeconomics🧠 ap psychology👩🏾‍⚖️ ap us government

english & capstone

✍🏽 ap english language📚 ap english literature🔍 ap research💬 ap seminar

arts

🎨 ap art & design🖼️ ap art history🎵 ap music theory

science

🧬 ap biology🧪 ap chemistry♻️ ap environmental science🎡 ap physics 1🧲 ap physics 2💡 ap physics c: e&m⚙️ ap physics c: mechanics

math & computer science

🧮 ap calculus ab♾️ ap calculus bc📐 ap precalculus📊 ap statistics💻 ap computer science a⌨️ ap computer science p

world languages

🇨🇳 ap chinese🇫🇷 ap french🇩🇪 ap german🇮🇹 ap italian🇯🇵 ap japanese🏛️ ap latin🇪🇸 ap spanish language💃🏽 ap spanish literature

career kickstart

💼 ap business with personal finance🔒 ap cybersecurity

go beyond AP

high school exams

✏️ PSAT🎓 Digital SAT🎒 ACT

honors classes

🍬 honors algebra II🫀 honors anatomy🐇 honors biology👩🏽‍🔬 honors chemistry💲 honors economics📐 honors geometry⚾️ honors physics📏 honors pre-calculus📊 honors statistics🗳️ honors us government🇺🇸 honors us history🌎 honors world history

college classes

👩🏽‍🎤 arts👔 business🎤 communications🏗️ engineering📓 humanities➗ math🧑🏽‍🔬 science💶 social science

hs classes

🏛️ alabama history⛰️ appalachian studies🌴 california history🌍 earth science🌐 ethnic studies🐊 florida history🍑 georgia history🌎 global studies🌺 hawaiian studies📰 journalism🪶 native american studies🌵 new mexico history🤠 oklahoma history⚗️ physical science🎙️ speech and debate🤝 texas government🤠 texas history🌲 washington state history🕊️ world religions
RefundsTermsPrivacyCCPAAI TransparencySchool Data Privacy

© 2026 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.