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the joint probability density function of the random variables X and Y is given by: f(x,y) = { 2x, 0<=x, y<=1                0, otherwise a) sketch the region on which the joint density function  is nonzerob) Calculate P(X<1/2, Y>1/2)c) Find the marginal probability density function of X and Yd) Determine whether X and Y are independente) Find the conditional density functions f(x|y) and f(y|x)f) Calculate the expected value of X and Yg) Find the covariance of X and Yh) Find the correlation coefficient of X and Y

the joint probability density function of the random variables X and Y is given by: f(x,y) = { 2x, 0<=x, y<=1                0, otherwise a) sketch the region on which the joint density function  is nonzerob) Calculate P(X<1/2, Y>1/2)c) Find the marginal probability density function of X and Yd) Determine whether X and Y are independente) Find the conditional density functions f(x|y) and f(y|x)f) Calculate the expected value of X and Yg) Find the covariance of X and Yh) Find the correlation coefficient of X and Y

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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the joint probability density function of the random variables X and Y is given by:

f(x,y) = { 2x, 0<=x, y<=1
                0, otherwise


a) sketch the region on which the joint density function  is nonzero
b) Calculate P(X<1/2, Y>1/2)
c) Find the marginal probability density function of X and Y
d) Determine whether X and Y are independent
e) Find the conditional density functions f(x|y) and f(y|x)
f) Calculate the expected value of X and Y
g) Find the covariance of X and Y
h) Find the correlation coefficient of X and Y

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