1.

The symmetric distribution having parameters as it's mean and variance is called as

Answer»

Let
X
have a uniform distribution on (,)
(
a
,
B
)
. The DENSITY function of
X
is

()=1−
f
(
x
)
=
1
b
−
a
if ≤≤
a
≤
x
≤
b
and 0
0
elsewhere

The the MEAN is GIVEN by

[]=∫−=2−22(−)=+2
E
[
X
]
=
∫
a
b
x
b
−
a
d
x
=
b
2
−
a
2
2
(
b
−
a
)
=
b
+
a
2

The variance is given by[2]−([])2
E
[
X
2
]
−
(
E
[
X
]
)
2

[2]=∫2−=3−33(−)=2++23
E
[
X
2
]
=
∫
a
b
x
2
b
−
a
d
x
=
b
3
−
a
3
3
(
b
−
a
)
=
b
2
+
b
a
+
a
2
3

The required variance is then

2++23−(+)24=(−)212
b
2
+
b
a
+
a
2
3
−
(
b
+
a
)
2
4
=
(
b
−
a
)
2
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1 comment from Dauren Baitursyn
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Hope this helps


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