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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 224
/
3
/
a
/
Solution
Codex
(
@codex,
0
)
...
Past exam of the mathematics course of the University of Cambridge
2022
iii
Paper 224
3
a
2026-09-28
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The
type
of
x
1
n
∈
A
n
is its empirical
mass
function
P
x
1
n
(
a
)
=
n
1
∑
i
=
1
n
1
{
x
i
=
a
}
,
a
∈
A
.
(1)
For
a
product source
Q
⊗
n
,
Q
⊗
n
(
x
1
n
)
=
i
=
1
∏
n
Q
(
x
i
)
=
a
∈
A
∏
Q
(
a
)
n
P
x
1
n
(
a
)
=
2
−
n
{
H
(
P
x
1
n
)
+
D
(
P
x
1
n
∥
Q
)}
,
(2)
with the usual convention that the
probability
is zero if the string
uses
a
symbol
outside the support of
Q
.
Ancestors
(11)
a
3
Paper 224
iii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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