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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?

A First Course in Probability (10th Edition)
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...
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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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