The joint density of X and Y is given by, 6. ху fxr (x, y) =-(x² + ) 7 0 1) b) Find the marginal probability distributions of X and Y. c) Find the conditional probability density function of Y given X=0.5 and calculate P(Y<1\X=0.5). d) Calculate the correlation coefficient. State whether X and Y are independent or not.
The joint density of X and Y is given by, 6. ху fxr (x, y) =-(x² + ) 7 0 1) b) Find the marginal probability distributions of X and Y. c) Find the conditional probability density function of Y given X=0.5 and calculate P(Y<1\X=0.5). d) Calculate the correlation coefficient. State whether X and Y are independent or not.
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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![3.
The joint density of X and Y is given by,
fxr (x, y) :
7
ху
+
0 <x < 1, 0 < y < 2
2
a) Calculate P(X<1, Y>1)
b) Find the marginal probability distributions of X and Y.
c) Find the conditional probability density function of Y given X=0.5 and calculate
P(Y<1\X=0.5).
d) Calculate the correlation coefficient. State whether X and Y are independent or not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9abaf73-be48-42b8-a308-b820fd695d3a%2F29cd15f0-56cf-439b-80b6-cdd0852f91b2%2Fp1nx6z6_processed.png&w=3840&q=75)
Transcribed Image Text:3.
The joint density of X and Y is given by,
fxr (x, y) :
7
ху
+
0 <x < 1, 0 < y < 2
2
a) Calculate P(X<1, Y>1)
b) Find the marginal probability distributions of X and Y.
c) Find the conditional probability density function of Y given X=0.5 and calculate
P(Y<1\X=0.5).
d) Calculate the correlation coefficient. State whether X and Y are independent or not.
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