Let X and Y be continuous random variables with the joint probability density function f (x, y) = 6x, 0 < x < y < 1. (a) Draw the domain of (X,Y) (b) Find the marginal probability density function of Y. (c) Find the conditional distribution fx|Y=y(x|Y = y) of X given Y = y.

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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 23E
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Let X and Y be continuous random variables with the joint probability density function
f (x, y) = 6x, 0 < x < y < 1.
(a) Draw the domain of (X, Y)
(b) Find the marginal probability density function of Y.
(c) Find the conditional distribution fx|Y=y(x|Y = y) of X given Y = y.
(d) The conditional expectation of X given Y
= y, denoted by E(X|Y = y), is defined to be
E(X|Y = y)
fx]Y=y(x|Y = y)dx
Find E(X|Y = y).
Transcribed Image Text:Let X and Y be continuous random variables with the joint probability density function f (x, y) = 6x, 0 < x < y < 1. (a) Draw the domain of (X, Y) (b) Find the marginal probability density function of Y. (c) Find the conditional distribution fx|Y=y(x|Y = y) of X given Y = y. (d) The conditional expectation of X given Y = y, denoted by E(X|Y = y), is defined to be E(X|Y = y) fx]Y=y(x|Y = y)dx Find E(X|Y = y).
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,