stick of length 1 on the x-a
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
Question
Mm6
![We place a stick of length 1 on the x-axis, from the
origin to the point (1, 0). We cut the stick into three
pieces at random, that is, the abscissas U and V of
the cuts are independent and evenly distributed
over the interval (0, 1). Let L1, L2, L3 be the lengths
of the leftmost piece, the middle piece and the
rightmost piece, respectively
We want to calculate the probability a so that we
can make a triangle with the three pieces 1.
a)
What is the event for which a is the probability?
b)
Express the random variables L1, L2 and L3 as a
function of U and V
c)
To show that
a = 2P (U < V, L1< 1/2, L2 <1/2, L3 <1/2)
d)
Calculate a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05043c29-3d5f-4328-adf1-091651cc3623%2Fc3a784d0-4474-4235-b954-6303258f4478%2F9ecjm5r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:We place a stick of length 1 on the x-axis, from the
origin to the point (1, 0). We cut the stick into three
pieces at random, that is, the abscissas U and V of
the cuts are independent and evenly distributed
over the interval (0, 1). Let L1, L2, L3 be the lengths
of the leftmost piece, the middle piece and the
rightmost piece, respectively
We want to calculate the probability a so that we
can make a triangle with the three pieces 1.
a)
What is the event for which a is the probability?
b)
Express the random variables L1, L2 and L3 as a
function of U and V
c)
To show that
a = 2P (U < V, L1< 1/2, L2 <1/2, L3 <1/2)
d)
Calculate a
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 6 steps with 31 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt