Answered: Consider X and Y are joint distributed…

Consider X and Y are joint distributed with PDF f(x,y)=x+y, 0≤x≤1, 0≤y≤1. (a) Find the probability that X > 0.5. (b)FindP(X> Y 1/2). (c) Are X and Y independent?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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Question

Consider X and Y are joint distributed with PDF
f(x,y)=x+y, 0≤x≤1, 0≤y≤1.

(a) Find the probability that X > 0.5.

(b)FindP(X> Y ^1/2^).
(c) Are X and Y independent?

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Expert Solution

Step 1: Given information

Consider $X$ and $Y$ are joint distributed with PDF is given by,

$f open parentheses x comma y close parentheses equals open curly brackets table row cell x plus y space space semicolon space 0 less or equal than x less or equal than 1 comma space 0 less or equal than y less or equal than 1 end cell row cell space space space space 0 space space space space semicolon space text otherwise end text end cell end table close$

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