Consider the pair of random variables ( X , Y ) with joint PDF f X , Y ( x , y ) = 2 for 0 ≤ x ≤ y ≤ 1 and f X , Y ( x , y ) = 0 otherwise. (In particular, note that the joint PDF is only nonzero when x ≤ y .) (a) Draw a picture of the range of ( X , Y ) in the x y -plane. (b) Describe the conditional distribution of X given Y = y , for 0 ≤ y ≤ 1 . (c) What is the marginal PDF f X of X ? (d) Are X and Y independent?
Consider the pair of random variables ( X , Y ) with joint PDF f X , Y ( x , y ) = 2 for 0 ≤ x ≤ y ≤ 1 and f X , Y ( x , y ) = 0 otherwise. (In particular, note that the joint PDF is only nonzero when x ≤ y .) (a) Draw a picture of the range of ( X , Y ) in the x y -plane. (b) Describe the conditional distribution of X given Y = y , for 0 ≤ y ≤ 1 . (c) What is the marginal PDF f X of X ? (d) Are X and Y independent?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Consider the pair of random variables
(
X
,
Y
)
with joint PDF
f
X
,
Y
(
x
,
y
)
=
2
for
0
≤
x
≤
y
≤
1
and
f
X
,
Y
(
x
,
y
)
=
0
otherwise. (In particular, note that the joint PDF is only nonzero when
x
≤
y
.)
(a) Draw a picture of the range of
(
X
,
Y
)
in the
x
y
-plane.
(b) Describe the conditional distribution of
X
given
Y
=
y
, for
0
≤
y
≤
1
.
(c) What is the marginal PDF
f
X
of
X
?
(d) Are
X
and
Y
independent?
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