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

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Chapter1: Combinatorial Analysis
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Let X and Y be independent random variables cach uniformly distributed on the unit interval (0, 1).
Find:
a) P (Y ≥ ¦ | Y ≥ 1 − 2X);
b) P(|XY| ≤ 0.25);
c) P (|X/Y - 1| ≤ 0.25);
d) P(Y ≥ XY ≥ 0.25).
Transcribed Image Text:Let X and Y be independent random variables cach uniformly distributed on the unit interval (0, 1). Find: a) P (Y ≥ ¦ | Y ≥ 1 − 2X); b) P(|XY| ≤ 0.25); c) P (|X/Y - 1| ≤ 0.25); d) P(Y ≥ XY ≥ 0.25).
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