Homework Help is Here – Start Your Trial Now!
Math
Probability
(b) A point P with coordinates (X, Y) is uniformly chosen from the unit disk D = {(x, y) : x² + y² ≤ 4}. What is the probability that the maximum of X, Y is lesser () than 1?

(b) A point P with coordinates (X, Y) is uniformly chosen from the unit disk D = {(x, y) : x² + y² ≤ 4}. What is the probability that the maximum of X, Y is lesser () than 1?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 51E
See similar textbooks
icon
Related questions
Question
(a) Let X exp(1), and Y = frac(X), the fractional part of X. Compute the probabiltiy P(Y > 0.5|X ≤ 1.5). Express your answer up to 3rd decimal place. (The fractional part of a nonnegative number X is defined as frac(X) X - [X], e.g., frac (3232.52) = 0.52, frac(1.232) = 0.232, frac(3) = 0, frac(7): = 0.14159265...) = (b) A point P with coordinates (X, Y) is uniformly chosen from the unit disk D = {(x, y) : x² + y² ≤ 4}. What is the probability that the maximum of X, Y is lesser (≤) than 1?
Transcribed Image Text:(a) Let X exp(1), and Y = frac(X), the fractional part of X. Compute the probabiltiy P(Y > 0.5|X ≤ 1.5). Express your answer up to 3rd decimal place. (The fractional part of a nonnegative number X is defined as frac(X) X - [X], e.g., frac (3232.52) = 0.52, frac(1.232) = 0.232, frac(3) = 0, frac(7): = 0.14159265...) = (b) A point P with coordinates (X, Y) is uniformly chosen from the unit disk D = {(x, y) : x² + y² ≤ 4}. What is the probability that the maximum of X, Y is lesser (≤) than 1?
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
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…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS