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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Please sir if you can't solve stepwise with explanation in each step and also given information and final answer Along with the concept and also showing excel formula (wherever needed) please skip , if yes pls solve ill definitely rate the solution and dont do handwritten...

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 1: Write the given information.

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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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