Databases Reference
In-Depth Information
A.7 Projects and Problems
1.
If
A
∩
B
=
φ
, show that
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
−
P
(
A
∩
B
)
2.
Show that expectation is a linear operator in both the discrete and the continuous case.
3.
If
a
is a constant, show that
E
[
a
]=
a
.
4.
Show that for a random variable
X
,
2
X
X
2
2
X
σ
=
E
[
]−
μ
5.
Show that the variance of the uniform distribution is given by
2
=
(
b
−
a
)
2
X
σ
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