2.8 Consider the triangular random variable with pdf 0 if x < 2a or x > 2b, if 2a < x
2.8 Consider the triangular random variable with pdf 0 if x < 2a or x > 2b, if 2a < x
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![2.8
Consider the triangular random variable with pdf
0
f(x) =
X
X
2a
(b − a)²
(2b − x)
(b − a)²
if x < 2a or x > 2b,
if 2a < x <a+b,
if a + b < x < 2b.
a) Derive the corresponding cdf F.
b) Show that applying the inverse-transform method yields
2a + (b-a)√2U
2b + (a − b) √2(1 – U)
if 0 <U</,
if <U < 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9eada888-ead5-4d59-98d2-e09b1da94bfc%2Fc7bcd2c5-3c6c-4258-bc49-dd87c669bd8c%2F9lwu1d9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.8
Consider the triangular random variable with pdf
0
f(x) =
X
X
2a
(b − a)²
(2b − x)
(b − a)²
if x < 2a or x > 2b,
if 2a < x <a+b,
if a + b < x < 2b.
a) Derive the corresponding cdf F.
b) Show that applying the inverse-transform method yields
2a + (b-a)√2U
2b + (a − b) √2(1 – U)
if 0 <U</,
if <U < 1.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 14 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![A First Course in Probability (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134753119/9780134753119_smallCoverImage.gif)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
![A First Course in Probability](https://www.bartleby.com/isbn_cover_images/9780321794772/9780321794772_smallCoverImage.gif)
![A First Course in Probability (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134753119/9780134753119_smallCoverImage.gif)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
![A First Course in Probability](https://www.bartleby.com/isbn_cover_images/9780321794772/9780321794772_smallCoverImage.gif)