AP Statistics Page 1 of 7 Study: Mean and Variances of Random Variables

Copyright 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright 1996, Texas Instruments, Incorporated.

Calculator Instructions for the TI-83 and TI-84

These instructions assume that you've read and followed the directions in the "Getting Started" chapter of your calculator manual. The steps covered in this guide are also covered in the "Statistics" chapter of your calculator manual.

Tex in a box, like this ON, is the name of a button on the calculator. Text in brackets, like this [L1], is a second function, shown in yellow above one of the

buttons. Text in bold, like this edit, is a command within a menu on the calculator screen.

Section 1:

Find the standard deviation for a proability distribution using your calculator.

This equation finds the standard deviation of X.

21 ix p

Use your calculator to find the Standard Deviation of X for this data set:

Shaq's Free Throw Pobability Distribution

X = # of points 0 1 2

P(X) .3025 .4950 .2025

Step 1: Clear List 1 through List 4.

1. Pres STAT 4.

2. Input 2nd [L1], 2nd [L2], 2nd [L3], 2nd [L4].

3. Press ENTER.

Your calculator says DONE.

Lists L1 through L4 are cleared.

Step 2: Enter the values of X in to L1.

1. Press STAT ENTER.

You are now in the Lists.

2. Input the values of X (number of free throw points) into L1.

Step 3: Generate 2ix for the values of X in L2.

1. Move your cursor over L2.

2. Input the formula (L1-.9)2

AP Statistics Page 2 of 7 Study: Mean and Variances of Random Variables

Copyright 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright 1996, Texas Instruments, Incorporated.

3. Press 2nd [L1] -.9 )x2

4. Press ENTER.

Your screen should now look like this:

Step 4: Enter the Values of P(X) into L3.

1. Input .3025, Press ENTER.

2. Continue entering the values of P(X) into L3.

Step 5: Multiply 2ix by the Values of P(X) in L4.

1. Move the cursor to the first entry in L3

2. Move your cursor over L4.

3. Press 2nd [L2] x 2nd [L3].

Your screen should now look like this:

Step 6: Generate the Variance for this data.

1. Press STAT.

2. Move your cursor over CALC.

3. Press ENTER.

This selects 1-Var Stats.

4. Press 2nd L4 ENTER.

The variance is x .

AP Statistics Page 3 of 7 Study: Mean and Variances of Random Variables

Copyright 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright 1996, Texas Instruments, Incorporated.

Your screen should look like this.

Step 7: Find the Standard Deviation for this data.

1. Press 2nd .

2. Input .495

3. Press ENTER.

This generates the square root for the variance, x , for L4.

Your screen should now look like this:

Section 2:

Verify a bx xb for the following data set.

X -2 0 1 5.2 5.5 6 6.8

X* -28 -14 -7 22.4 24.5 28 33.6

In this data set, for X* each value of X has had 2 subtracted from it and then been multiplied by 7:

Step 1: Clear List 1 through List 4.

1. Press STAT 4.

2. Input 2nd [L1], 2nd [L2], 2nd [L3], 2nd [L4].

AP Statistics Page 4 of 7 Study: Mean and Variances of Random Variables

Copyright 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright 1996, Texas Instruments, Incorporated.

3. Press ENTER.

Your calculator says DONE.

Lists L1 through L4 are cleared.

Step 2: Find for X.

1. Enter the values of X into L1.

2. Press STAT.

3. Move your cursor over to CALC.

4. Press ENTER.

This selects 1-Var Stats.

5. Press 2nd [L1] ENTER.

Your calculator generates the solution for x .

Step 3: Find for X*.

1. Enter the values of X* into L2.

2. Press STAT.

3. Move your cursor over to CALC.

4. Press ENTER.

This selects 1-Var Stats.

5. Press 2nd [L2] ENTER.

Your calculator generates the solution for 2 7 .X

AP Statistics Page 5 of 7 Study: Mean and Variances of Random Variables

Copyright 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright 1996, Texas Instruments, Incorporated.

Proofs

You aren't required to know any of the following proofs, but they can help you understand how we get the formulas for:

1. linear transformation of a random variable.

2. the mean of the sum of two random variables.

3. the standard deviation of the sum of two random variables.

AP Statistics Page 6 of 7 Study: Mean and Variances of Random Variables

Copyright 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright 1996, Texas Instruments, Incorporated.

Directions

Use this guide to take notes while you watch the tutorial. Keep your completed study guide in your notebook for later study. Key Terms and Concepts continuous random variable discrete random variable expected value linear transformation of a discrete

random variable mean of a discrete random variable

probability distribution random variable standard deviation of discrete random

variable variance of a discrete random variable

Tutorial Sections

Mean of a Discrete Random Variable Variance and Standard Deviation of a Discrete Random Variable

AP Statistics Page 7 of 7 Study: Mean and Variances of Random Variables

Copyright 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright 1996, Texas Instruments, Incorporated.

Rules for Means Rules for Variances and Standard Deviations