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Question 3 - Week 3 Practice | Prasnya
Q3
00:00
3 Aug 2025
Q3.
Suppose
X
1
,
X
2
,
X
3
∼
X_1,X_2,X_3\sim
X
1
,
X
2
,
X
3
∼
i.i.d.
X
X
X
such that
E
[
X
]
=
10
E[X]=10
E
[
X
]
=
10
and
Var
(
X
)
=
4
\operatorname{Var}(X)=4
Var
(
X
)
=
4
. Define
Y
=
X
1
−
X
2
+
X
3
Y=X_1-X_2+X_3
Y
=
X
1
−
X
2
+
X
3
and
Z
=
2
Y
Z=2Y
Z
=
2
Y
. Choose the correct option(s).
A
E
[
Z
]
=
10
E[Z]=10
E
[
Z
]
=
10
B
Var
(
Z
)
=
48
\operatorname{Var}(Z)=48
Var
(
Z
)
=
48
C
Var
(
Z
)
=
24
\operatorname{Var}(Z)=24
Var
(
Z
)
=
24
D
E
[
Z
]
=
20
E[Z]=20
E
[
Z
]
=
20
Save
Check
Details
Q3
00:00
3 Aug 2025
Q3.
Suppose
X
1
,
X
2
,
X
3
∼
X_1,X_2,X_3\sim
X
1
,
X
2
,
X
3
∼
i.i.d.
X
X
X
such that
E
[
X
]
=
10
E[X]=10
E
[
X
]
=
10
and
Var
(
X
)
=
4
\operatorname{Var}(X)=4
Var
(
X
)
=
4
. Define
Y
=
X
1
−
X
2
+
X
3
Y=X_1-X_2+X_3
Y
=
X
1
−
X
2
+
X
3
and
Z
=
2
Y
Z=2Y
Z
=
2
Y
. Choose the correct option(s).
A
E
[
Z
]
=
10
E[Z]=10
E
[
Z
]
=
10
B
Var
(
Z
)
=
48
\operatorname{Var}(Z)=48
Var
(
Z
)
=
48
C
Var
(
Z
)
=
24
\operatorname{Var}(Z)=24
Var
(
Z
)
=
24
D
E
[
Z
]
=
20
E[Z]=20
E
[
Z
]
=
20
Save
Check
Details
