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Question 23 - Week 3 Practice | Prasnya
Q23
00:00
6 Aug 2023
Q23.
Suppose
X
1
,
X
2
,
X
3
,
X
4
∼
i.i.d.
X
X_1,X_2,X_3,X_4\sim \text{i.i.d. }X
X
1
,
X
2
,
X
3
,
X
4
∼
i.i.d.
X
with
E
[
X
]
=
10
E[X]=10
E
[
X
]
=
10
and
Var
(
X
)
=
4
\operatorname{Var}(X)=4
Var
(
X
)
=
4
. Define
S
=
2
X
1
−
2
X
2
−
X
3
+
3
X
4
S=2X_1-2X_2-X_3+3X_4
S
=
2
X
1
−
2
X
2
−
X
3
+
3
X
4
. Choose the correct option(s) from below:
A
E
[
S
]
=
20
E[S]=20
E
[
S
]
=
20
B
Var
(
S
)
=
52
\operatorname{Var}(S)=52
Var
(
S
)
=
52
C
Var
(
S
)
=
72
\operatorname{Var}(S)=72
Var
(
S
)
=
72
D
E
[
S
]
=
180
E[S]=180
E
[
S
]
=
180
Save
Check
Details
Q23
00:00
6 Aug 2023
Q23.
Suppose
X
1
,
X
2
,
X
3
,
X
4
∼
i.i.d.
X
X_1,X_2,X_3,X_4\sim \text{i.i.d. }X
X
1
,
X
2
,
X
3
,
X
4
∼
i.i.d.
X
with
E
[
X
]
=
10
E[X]=10
E
[
X
]
=
10
and
Var
(
X
)
=
4
\operatorname{Var}(X)=4
Var
(
X
)
=
4
. Define
S
=
2
X
1
−
2
X
2
−
X
3
+
3
X
4
S=2X_1-2X_2-X_3+3X_4
S
=
2
X
1
−
2
X
2
−
X
3
+
3
X
4
. Choose the correct option(s) from below:
A
E
[
S
]
=
20
E[S]=20
E
[
S
]
=
20
B
Var
(
S
)
=
52
\operatorname{Var}(S)=52
Var
(
S
)
=
52
C
Var
(
S
)
=
72
\operatorname{Var}(S)=72
Var
(
S
)
=
72
D
E
[
S
]
=
180
E[S]=180
E
[
S
]
=
180
Save
Check
Details
