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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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Question

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

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

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