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Question 52 - Week 5 Practice | Prasnya
Q52
00:00
3 Dec 2024
Q52.
Let
(
X
,
Y
)
∼
U
n
i
f
o
r
m
(
D
)
(X,Y)\sim \mathrm{Uniform}(D)
(
X
,
Y
)
∼
Uniform
(
D
)
, where
D
=
{
(
x
,
y
)
:
x
+
y
<
3
,
x
>
0
,
y
>
0
}
D=\{(x,y):x+y<3,\ x>0,\ y>0\}
D
=
{(
x
,
y
)
:
x
+
y
<
3
,
x
>
0
,
y
>
0
}
. What is the marginal density function of
f
X
(
x
)
f_X(x)
f
X
(
x
)
?
A
f
X
(
x
)
=
2
9
(
3
−
x
)
f_X(x)=\frac{2}{9}(3-x)
f
X
(
x
)
=
9
2
(
3
−
x
)
,
0
<
x
<
3
0<x<3
0
<
x
<
3
;
0
0
0
otherwise
B
f
X
(
x
)
=
3
2
(
3
−
x
)
f_X(x)=\frac{3}{2}(3-x)
f
X
(
x
)
=
2
3
(
3
−
x
)
,
0
<
x
<
3
0<x<3
0
<
x
<
3
;
0
0
0
otherwise
C
f
X
(
x
)
=
9
2
(
3
−
x
)
f_X(x)=\frac{9}{2}(3-x)
f
X
(
x
)
=
2
9
(
3
−
x
)
,
0
<
x
<
3
0<x<3
0
<
x
<
3
;
0
0
0
otherwise
D
f
X
(
x
)
=
2
(
3
−
x
)
f_X(x)=2(3-x)
f
X
(
x
)
=
2
(
3
−
x
)
,
0
<
x
<
3
0<x<3
0
<
x
<
3
;
0
0
0
otherwise
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Check
Details
Q52
00:00
3 Dec 2024
Q52.
Let
(
X
,
Y
)
∼
U
n
i
f
o
r
m
(
D
)
(X,Y)\sim \mathrm{Uniform}(D)
(
X
,
Y
)
∼
Uniform
(
D
)
, where
D
=
{
(
x
,
y
)
:
x
+
y
<
3
,
x
>
0
,
y
>
0
}
D=\{(x,y):x+y<3,\ x>0,\ y>0\}
D
=
{(
x
,
y
)
:
x
+
y
<
3
,
x
>
0
,
y
>
0
}
. What is the marginal density function of
f
X
(
x
)
f_X(x)
f
X
(
x
)
?
A
f
X
(
x
)
=
2
9
(
3
−
x
)
f_X(x)=\frac{2}{9}(3-x)
f
X
(
x
)
=
9
2
(
3
−
x
)
,
0
<
x
<
3
0<x<3
0
<
x
<
3
;
0
0
0
otherwise
B
f
X
(
x
)
=
3
2
(
3
−
x
)
f_X(x)=\frac{3}{2}(3-x)
f
X
(
x
)
=
2
3
(
3
−
x
)
,
0
<
x
<
3
0<x<3
0
<
x
<
3
;
0
0
0
otherwise
C
f
X
(
x
)
=
9
2
(
3
−
x
)
f_X(x)=\frac{9}{2}(3-x)
f
X
(
x
)
=
2
9
(
3
−
x
)
,
0
<
x
<
3
0<x<3
0
<
x
<
3
;
0
0
0
otherwise
D
f
X
(
x
)
=
2
(
3
−
x
)
f_X(x)=2(3-x)
f
X
(
x
)
=
2
(
3
−
x
)
,
0
<
x
<
3
0<x<3
0
<
x
<
3
;
0
0
0
otherwise
Save
Check
Details
