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Question 9 - Week 7 Practice | Prasnya
Q9
00:00
10 Jul 2022
Q9.
Compute the expected value and variance of the sample mean
X
ˉ
=
X
1
+
⋯
+
X
n
n
\bar X=\frac{X_1+\cdots+X_n}{n}
X
ˉ
=
n
X
1
+
⋯
+
X
n
.
@passage
A
E
[
X
ˉ
]
=
0
E[\bar X]=0
E
[
X
ˉ
]
=
0
and
V
a
r
(
X
ˉ
)
=
0
\mathrm{Var}(\bar X)=0
Var
(
X
ˉ
)
=
0
B
E
[
X
ˉ
]
=
0
E[\bar X]=0
E
[
X
ˉ
]
=
0
and
V
a
r
(
X
ˉ
)
=
1
/
12
\mathrm{Var}(\bar X)=1/12
Var
(
X
ˉ
)
=
1/12
C
E
[
X
ˉ
]
=
1
/
2
E[\bar X]=1/2
E
[
X
ˉ
]
=
1/2
and
V
a
r
(
X
ˉ
)
=
1
/
n
\mathrm{Var}(\bar X)=1/n
Var
(
X
ˉ
)
=
1/
n
D
E
[
X
ˉ
]
=
0
E[\bar X]=0
E
[
X
ˉ
]
=
0
and
V
a
r
(
X
ˉ
)
=
1
/
(
12
n
)
\mathrm{Var}(\bar X)=1/(12n)
Var
(
X
ˉ
)
=
1/
(
12
n
)
Save
Read
Check
Details
Q9
00:00
10 Jul 2022
Q9.
Compute the expected value and variance of the sample mean
X
ˉ
=
X
1
+
⋯
+
X
n
n
\bar X=\frac{X_1+\cdots+X_n}{n}
X
ˉ
=
n
X
1
+
⋯
+
X
n
.
@passage
A
E
[
X
ˉ
]
=
0
E[\bar X]=0
E
[
X
ˉ
]
=
0
and
V
a
r
(
X
ˉ
)
=
0
\mathrm{Var}(\bar X)=0
Var
(
X
ˉ
)
=
0
B
E
[
X
ˉ
]
=
0
E[\bar X]=0
E
[
X
ˉ
]
=
0
and
V
a
r
(
X
ˉ
)
=
1
/
12
\mathrm{Var}(\bar X)=1/12
Var
(
X
ˉ
)
=
1/12
C
E
[
X
ˉ
]
=
1
/
2
E[\bar X]=1/2
E
[
X
ˉ
]
=
1/2
and
V
a
r
(
X
ˉ
)
=
1
/
n
\mathrm{Var}(\bar X)=1/n
Var
(
X
ˉ
)
=
1/
n
D
E
[
X
ˉ
]
=
0
E[\bar X]=0
E
[
X
ˉ
]
=
0
and
V
a
r
(
X
ˉ
)
=
1
/
(
12
n
)
\mathrm{Var}(\bar X)=1/(12n)
Var
(
X
ˉ
)
=
1/
(
12
n
)
Save
Read
Check
Details
