A First Course in Probability (10th Edition)
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ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![Compute the expected values using the given joint probability density function over the specified region:
4-Z
4
4-z-2y
2
E(X)= f*f*
= √₁² √ ² ²
xyz²dx dy dz
0 0
0
4-Z
2
- 55
0 0
=
E(Y) =
X=1
=
IN
315
512
315
512
=
=
E(Z) = S
11
315
512
0 0
5² 5²
0 0
-
4-Z
2
4
√
0 0
3
2
315
512
0 0
4-Z
2
4
512 o o
4-Z
4
x²
= 315 √ √ [*]
2 y²z²
2
0
Jo
Y=1/1/2
0 0
0
4-Z
2
315
512
₁-2-²x²yz²dx dy dz
0
4-Z
2
yz
·[*[²²²²-²-²2, 315 xyz²dx dy diz
Z.
0
4-Z
2
X.
4-z-2y 315
y'
512
x³
14-z-2y
3 Jo
yz³
²-2-2% xy²z²dx dy dz
0
dy dz
xyz²dx dy dz
274-z-2y
5²
²
1-2-24 xyz³dx dy dz
0
dy dz
x² 74-z-2y
2 Jo
dy dz](https://content.bartleby.com/qna-images/question/03b5f08a-ed30-4408-a657-de0de7174de5/c93e30fb-ffc8-4311-90f0-faa17b8c95ab/j1ei3bo_processed.png)
Transcribed Image Text:Compute the expected values using the given joint probability density function over the specified region:
4-Z
4
4-z-2y
2
E(X)= f*f*
= √₁² √ ² ²
xyz²dx dy dz
0 0
0
4-Z
2
- 55
0 0
=
E(Y) =
X=1
=
IN
315
512
315
512
=
=
E(Z) = S
11
315
512
0 0
5² 5²
0 0
-
4-Z
2
4
√
0 0
3
2
315
512
0 0
4-Z
2
4
512 o o
4-Z
4
x²
= 315 √ √ [*]
2 y²z²
2
0
Jo
Y=1/1/2
0 0
0
4-Z
2
315
512
₁-2-²x²yz²dx dy dz
0
4-Z
2
yz
·[*[²²²²-²-²2, 315 xyz²dx dy diz
Z.
0
4-Z
2
X.
4-z-2y 315
y'
512
x³
14-z-2y
3 Jo
yz³
²-2-2% xy²z²dx dy dz
0
dy dz
xyz²dx dy dz
274-z-2y
5²
²
1-2-24 xyz³dx dy dz
0
dy dz
x² 74-z-2y
2 Jo
dy dz
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