Suppose X and Y are continuous random variables with the joint probability density function fx,y (x, y) = [2, if x > 0, y > 0, x + y < 1, otherwise. (a) Find Pr(X + Y <0.5) (b) Find the correlation Cor (X, Y). Are X and Y independent? Explain.

Suppose X and Y are continuous random variables with the joint probability density function fx,y (x, y) = [2, if x > 0, y > 0, x + y < 1, otherwise. (a) Find Pr(X + Y <0.5) (b) Find the correlation Cor (X, Y). Are X and Y independent? Explain.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Suppose X and Y are continuous random variables with the joint probability density
function
fx,y (x, y)
=
2, if x > 0, y > 0, x+y< 1,
0,
otherwise.
(a) Find Pr(X+Y < 0.5)
(b) Find the correlation Cor (X, Y). Are X and Y independent? Explain.

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Step 2: Determine the P(X + Y < 0.50).

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Step 3: Determine the value of E(X,Y).

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Step 4: Determine the value of E(X), E(Y) and their variances.

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Step 5: Determine the value of Cor(X,Y).

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