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(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 for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 53PS
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(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?
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