# Activities

• • ##### Subject Area

• Standard: VCE: Specialist Mathematics: Specialist Mathematics

• ##### Author Aust Senior

30 Minutes

• ##### Device
• TI-Nspire™ CAS
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™ CAS
TI-Nspire™ CAS Navigator™ NC System

4.2

• ##### Report an Issue

Linear Transformations of a Random Variable #### Activity Overview

This activity presents an intuitive approach to Linear Transformations of a random variable. If your students don’t understand E(aX+b) or Var(aX+b) then this is a good place to start. By building on a simple familiar example students can validate their intuition using the tables, graphs, spreadsheets and notation to build an better understanding of E(aX+b) and Var(aX+b).

#### Objectives

Understand linear combinations of random variables including:

• E(aX+b)=a.E(X)+b
• Var(aX+b)=a2.Var(X)

#### Vocabulary

Expected value, mean, variance, standard deviation, random variable, translation, transformation

#### About the Lesson

Students use their intuition to reason what would happen to the expected value for a regular die if two extra dots were added to each side. This intuition is then backed up by performing the calculations by hand and then generalised using an interactive slider that generates the updated computations, followed by the general solution with the assistance of CAS. Interactive graphs are also used to help visualise the process.