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Question 21 - Week 5 Practice | Prasnya
Q21
00:00
16 Mar 2025
Q21.
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
<
2
,
x
>
0
,
y
>
0
}
D=\{(x,y):x+y<2,x>0,y>0\}
D
=
{(
x
,
y
)
:
x
+
y
<
2
,
x
>
0
,
y
>
0
}
. What is the marginal density function of
X
X
X
?
A
f
X
(
x
)
=
{
1
2
(
2
−
x
)
,
0
<
x
<
2
;
0
otherwise
}
f_X(x)=\{\frac12(2-x),\ 0<x<2;\ 0\text{ otherwise}\}
f
X
(
x
)
=
{
2
1
(
2
−
x
)
,
0
<
x
<
2
;
0
otherwise
}
B
f
X
(
x
)
=
{
1
2
(
1
−
x
)
,
0
<
x
<
2
;
0
otherwise
}
f_X(x)=\{\frac12(1-x),\ 0<x<2;\ 0\text{ otherwise}\}
f
X
(
x
)
=
{
2
1
(
1
−
x
)
,
0
<
x
<
2
;
0
otherwise
}
C
f
X
(
x
)
=
{
2
−
x
,
0
<
x
<
2
;
0
otherwise
}
f_X(x)=\{2-x,\ 0<x<2;\ 0\text{ otherwise}\}
f
X
(
x
)
=
{
2
−
x
,
0
<
x
<
2
;
0
otherwise
}
D
f
X
(
x
)
=
{
1
,
0
<
x
<
2
;
0
otherwise
}
f_X(x)=\{1,\ 0<x<2;\ 0\text{ otherwise}\}
f
X
(
x
)
=
{
1
,
0
<
x
<
2
;
0
otherwise
}
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Check
Details
Q21
00:00
16 Mar 2025
Q21.
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
<
2
,
x
>
0
,
y
>
0
}
D=\{(x,y):x+y<2,x>0,y>0\}
D
=
{(
x
,
y
)
:
x
+
y
<
2
,
x
>
0
,
y
>
0
}
. What is the marginal density function of
X
X
X
?
A
f
X
(
x
)
=
{
1
2
(
2
−
x
)
,
0
<
x
<
2
;
0
otherwise
}
f_X(x)=\{\frac12(2-x),\ 0<x<2;\ 0\text{ otherwise}\}
f
X
(
x
)
=
{
2
1
(
2
−
x
)
,
0
<
x
<
2
;
0
otherwise
}
B
f
X
(
x
)
=
{
1
2
(
1
−
x
)
,
0
<
x
<
2
;
0
otherwise
}
f_X(x)=\{\frac12(1-x),\ 0<x<2;\ 0\text{ otherwise}\}
f
X
(
x
)
=
{
2
1
(
1
−
x
)
,
0
<
x
<
2
;
0
otherwise
}
C
f
X
(
x
)
=
{
2
−
x
,
0
<
x
<
2
;
0
otherwise
}
f_X(x)=\{2-x,\ 0<x<2;\ 0\text{ otherwise}\}
f
X
(
x
)
=
{
2
−
x
,
0
<
x
<
2
;
0
otherwise
}
D
f
X
(
x
)
=
{
1
,
0
<
x
<
2
;
0
otherwise
}
f_X(x)=\{1,\ 0<x<2;\ 0\text{ otherwise}\}
f
X
(
x
)
=
{
1
,
0
<
x
<
2
;
0
otherwise
}
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Check
Details
