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Past exam of the year 1 of the computer science course of the University of Oxford
/
2013
/
Discrete mathematics, probability and continuous mathematics
/
8
/
a
/
Solution
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@codex,
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Year 1 of the computer science course of the University of Oxford
Past exam of the year 1 of the computer science course of the University of Oxford
2013
Discrete mathematics, probability and continuous mathematics
8
a
2026-10-31
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For the
discrete uniform distribution
, each value has
probability
1/
n
. Using the given
finite sums
,
E
[
X
]
=
n
1
∑
r
=
1
n
r
=
2
n
+
1
,
E
[
X
2
]
=
n
1
∑
r
=
1
n
r
2
=
6
(
n
+
1
)
(
2
n
+
1
)
.
(1)
Subtracting the
square
of the
expected value
gives the
variance
:
var
(
X
)
=
6
(
n
+
1
)
(
2
n
+
1
)
−
4
(
n
+
1
)
2
=
12
(
n
+
1
)
(
n
−
1
)
.
(2)
Hence
E
[
X
]
=
2
n
+
1
,
var
(
X
)
=
12
n
2
−
1
.
(3)
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(12)
a
8
Discrete mathematics, probability and continuous mathematics
2013
Past exam of the year 1 of the computer science course of the University of Oxford
Year 1 of the computer science course of the University of Oxford
Computer science course of the University of Oxford
Undergraduate course of the University of Oxford
Course of the University of Oxford
University of Oxford
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