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Byju's Answer
Standard XII
Mathematics
Applications of Dot Product
For a Poissio...
Question
For a Poission distribution, which of the following is true
A
M
e
a
n
=
M
o
d
e
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B
M
e
d
i
a
n
=
S
.
D
.
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C
M
e
a
n
=
V
a
r
i
a
n
c
e
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D
M
e
d
i
a
n
=
V
a
r
i
a
n
c
e
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Solution
The correct option is
C
M
e
a
n
=
V
a
r
i
a
n
c
e
For Poission distribution we have
P
(
r
)
=
e
−
π
λ
r
r
i
(
r
=
0
,
1
,
2
,
.
.
.
∞
)
mean
=
∑
f
i
x
i
∑
f
i
=
∞
∑
r
=
0
r
P
(
r
)
,
∑
f
i
P
(
r
)
=
1
=
0
+
λ
e
−
λ
+
2
λ
2
e
−
λ
2
!
+
3
λ
3
e
−
λ
3
!
+
.
.
.
.
.
∞
=
λ
e
−
λ
(
1
+
λ
11
+
λ
2
2
!
+
λ
3
3
!
+
.
.
.
.
.
∞
)
=
λ
e
λ
.
e
λ
=
λ
similarly,
o
2
=
Variance
=
∑
∞
r
=
0
r
2
P
(
r
)
−
(
∑
∞
r
=
0
r
P
(
r
)
)
2
=
λ
e
λ
(
e
−
λ
+
λ
e
−
λ
)
−
λ
2
=
λ
=
mean
∴
mean
=
variance
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