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Question 27 - Week 5 Practice | Prasnya
Q27
00:00
1 Dec 2024
Q27.
Let
X
1
,
X
2
,
…
,
X
10
X_1,X_2,\ldots,X_{10}
X
1
,
X
2
,
…
,
X
10
be i.i.d. random variables with common MGF
M
X
(
λ
)
M_X(\lambda)
M
X
(
λ
)
. Find the MGF of
X
ˉ
\bar X
X
ˉ
, where
X
ˉ
=
(
X
1
+
⋯
+
X
10
)
/
10
\bar X=(X_1+\cdots+X_{10})/10
X
ˉ
=
(
X
1
+
⋯
+
X
10
)
/10
.
A
M
X
(
λ
/
10
)
M_X(\lambda/10)
M
X
(
λ
/10
)
B
(
M
X
(
λ
)
)
10
(M_X(\lambda))^{10}
(
M
X
(
λ
)
)
10
C
M
X
ˉ
(
λ
/
10
)
10
M_{\bar X}(\lambda/10)^{10}
M
X
ˉ
(
λ
/10
)
10
D
(
M
X
(
λ
/
10
)
)
10
(M_X(\lambda/10))^{10}
(
M
X
(
λ
/10
)
)
10
Save
Check
Details
Q27
00:00
1 Dec 2024
Q27.
Let
X
1
,
X
2
,
…
,
X
10
X_1,X_2,\ldots,X_{10}
X
1
,
X
2
,
…
,
X
10
be i.i.d. random variables with common MGF
M
X
(
λ
)
M_X(\lambda)
M
X
(
λ
)
. Find the MGF of
X
ˉ
\bar X
X
ˉ
, where
X
ˉ
=
(
X
1
+
⋯
+
X
10
)
/
10
\bar X=(X_1+\cdots+X_{10})/10
X
ˉ
=
(
X
1
+
⋯
+
X
10
)
/10
.
A
M
X
(
λ
/
10
)
M_X(\lambda/10)
M
X
(
λ
/10
)
B
(
M
X
(
λ
)
)
10
(M_X(\lambda))^{10}
(
M
X
(
λ
)
)
10
C
M
X
ˉ
(
λ
/
10
)
10
M_{\bar X}(\lambda/10)^{10}
M
X
ˉ
(
λ
/10
)
10
D
(
M
X
(
λ
/
10
)
)
10
(M_X(\lambda/10))^{10}
(
M
X
(
λ
/10
)
)
10
Save
Check
Details
