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Entropy of a sum of independent finite-group variables
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Mathematics
Area of mathematics
Probability and statistics
Information theory
Conditional entropy
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Words: 28
If
independent random variables
X
,
Y
take values in a
finite additive group
, then
H
(
X
+
Y
)
≥
max
{
H
(
X
)
,
H
(
Y
)}
.
(142)
Indeed,
H
(
X
+
Y
)
≥
H
(
X
+
Y
∣
Y
)
=
H
(
X
)
, and symmetrically for
Y
. Independence is essential: taking
Y
=
−
X
makes the sum constant.
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Conditional entropy
Information theory
Probability and statistics
Area of mathematics
Mathematics
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