Question

To generate values of a random variable that has the probability density function $\begin{equation} f(x) = \begin{cases} 1/4 & \text{if } -1 < x \le 1, \\ 1/6 & \text{if } 1 < x \le 4, \\ 0 & \text{otherwise.} \end{cases} \end{equation}$ (a) Describe clearly and specifically how to apply the inverse transformation method. Derive all involved equations. (b) Generate two values based on (a). (Note: Use RAND() in Excel for random numbers and make sure that you write them down in your solution.)

          To generate values of a random variable that has the probability density function
$\begin{equation*} f(x) = \begin{cases} 1/4 & \text{if } -1 < x \le 1, \\ 1/6 & \text{if } 1 < x \le 4, \\ 0 & \text{otherwise.} \end{cases} \end{equation*}$
(a) Describe clearly and specifically how to apply the inverse transformation method.
Derive all involved equations.
(b) Generate two values based on (a). (Note: Use RAND() in Excel for random numbers
and make sure that you write them down in your solution.)

Show more…

To generate values of a random variable that has the probability density function
f(x) = 1/4 if -1 < x ≤ 1,
1/6 if 1 < x ≤ 4,
0 otherwise.
(a) Describe clearly and specifically how to apply the inverse transformation method.
Derive all involved equations.
(b) Generate two values based on (a). (Note: Use RAND() in Excel for random numbers
and make sure that you write them down in your solution.)

Added by Asunci-N P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

01/26/2023

Step 1

For -1 < x < 1: F(x) = ∫(1/4)dx = (1/4)x | from -1 to x = (1/4)x - (-1/4) = (1/4)x + 1/4 For 1 < x < 4: F(x) = ∫(1/6)dx = (1/6)x | from 1 to x = (1/6)x - (1/6) = (1/6)x - 1/6 Step 2: Inverse of the CDF to generate random values. To generate random values using Show more…

Show all steps

lock

Thanks for your feedback!

To generate values of a random variable that has the probability density function (1/4 if -1<x<1, f(x)=1/6 if 1<x<4, 0 otherwise. (a) Describe clearly and specifically how to apply the inverse transformation method. Derive all involved equations. (b) Generate two values based on (a). (Note: Use RAND() in Excel for random numbers and make sure that you write them down in your solution.)

Play audio

Feedback

Powered by NumerAI

Sri K and 98 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later