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Suppose you choose two numbers x and y uniformly and independently at random from the unit interval [0, 1]. Find the probability that max {x, y} < 0.9. Hint: Try these cases. What if yx? Then max {x,y} = x in this case. What if y> x ? Then max {x, y} = y in this case. .81 Find the probability that max {x, y} < 0.9 given that y< 0.7. 0.9 Find the probability that max {x,y} < 0.9 given that y ≥ 0.7. 0.6 Find the probability that max {x, y} < 0.9 given that y ≤ (0.2x). --- B

Suppose you choose two numbers x and y uniformly and independently at random from the unit interval [0, 1]. Find the probability that max {x, y} < 0.9. Hint: Try these cases. What if yx? Then max {x,y} = x in this case. What if y> x ? Then max {x, y} = y in this case. .81 Find the probability that max {x, y} < 0.9 given that y< 0.7. 0.9 Find the probability that max {x,y} < 0.9 given that y ≥ 0.7. 0.6 Find the probability that max {x, y} < 0.9 given that y ≤ (0.2x). --- B

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose you choose two numbers x and y uniformly and independently at random from the unit interval [0, 1]. Find the probability that max {x, y} < 0.9. Hint: Try these cases. What if y ≤ x? Then max {x,y} = x in this case. What if y > x? Then max {x, y} .81 --- = = y in this case. Find the probability that max {x, y} < 0.9 given that y < 0.7. 0.9 Find the probability that max {x, y} < 0.9 given that y ≥ 0.7. 0.6 --- - Find the probability that max {x, y} < 0.9 given that y ≤ (0.2x).
Transcribed Image Text:Suppose you choose two numbers x and y uniformly and independently at random from the unit interval [0, 1]. Find the probability that max {x, y} < 0.9. Hint: Try these cases. What if y ≤ x? Then max {x,y} = x in this case. What if y > x? Then max {x, y} .81 --- = = y in this case. Find the probability that max {x, y} < 0.9 given that y < 0.7. 0.9 Find the probability that max {x, y} < 0.9 given that y ≥ 0.7. 0.6 --- - Find the probability that max {x, y} < 0.9 given that y ≤ (0.2x).
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