please show work and answers with neat handwriting. Let X and Y be independent random variables cach uniformly distributed on the unit interval (0, 1).Find:a) P (Y ≥ ½ | Y ≥ 1 – 2X);b) P(|XY| ≤ 0.25);c) P(|X/Y - 1| ≤ 0.25);d) P(Y ≥ X|Y ≥ 0.25).

The provided information is as follows:The be independent random variable each uniformly…

Answered: Let X and Y be independent random…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Let X and Y be independent random variables each uniformly distributed on the unit interval (0, 1). Find: a) P (Y ≥ ¼ | Y ≥ 1 – 2X); b) P(|XY| ≤ 0.25); c) P(|X/Y - 1| ≤ 0.25); d) P(Y ≥ XY ≥ 0.25).