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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?

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?

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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  1. 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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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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