Mixing
The monotonicity of a weighted entropy
$begingroup$
Now we have $$p(x) = frac{d!}{x!,(d-x)!,2^d}$$ $$e(x)=frac{x}{d}logBigg(frac{d}{x}Bigg) + frac{d-x}{d}log{frac{d}{d-x}}$$ and $$E(d) = sum_{0 < x < d}{p(x)e(x)}$$
How to prove the monotonicity of $E(d)$?
linear-algebra probability sequences-and-series combinatorics limits
asked Jan 23 at 20:42
user6180959user6180959
112
$endgroup$
add a comment |
$begingroup$
Now we have $$p(x) = frac{d!}{x!,(d-x)!,2^d}$$ $$e(x)=frac{x}{d}logBigg(frac{d}{x}Bigg) + frac{d-x}{d}log{frac{d}{d-x}}$$ and $$E(d) = sum_{0 < x < d}{p(x)e(x)}$$
How to prove the monotonicity of $E(d)$?
linear-algebra probability sequences-and-series combinatorics limits
asked Jan 23 at 20:42
user6180959user6180959
112
$endgroup$
1
$begingroup$
@Elborito 0 < x < d, I have edited the problem, please refer to the newest version :)
$endgroup$
– user6180959
Feb 8 at 4:32
add a comment |
$begingroup$
Now we have $$p(x) = frac{d!}{x!,(d-x)!,2^d}$$ $$e(x)=frac{x}{d}logBigg(frac{d}{x}Bigg) + frac{d-x}{d}log{frac{d}{d-x}}$$ and $$E(d) = sum_{0 < x < d}{p(x)e(x)}$$
How to prove the monotonicity of $E(d)$?
linear-algebra probability sequences-and-series combinatorics limits
asked Jan 23 at 20:42
user6180959user6180959
112
$endgroup$
Now we have $$p(x) = frac{d!}{x!,(d-x)!,2^d}$$ $$e(x)=frac{x}{d}logBigg(frac{d}{x}Bigg) + frac{d-x}{d}log{frac{d}{d-x}}$$ and $$E(d) = sum_{0 < x < d}{p(x)e(x)}$$
How to prove the monotonicity of $E(d)$?
linear-algebra probability sequences-and-series combinatorics limits
linear-algebra probability sequences-and-series combinatorics limits
asked Jan 23 at 20:42
user6180959user6180959
112
asked Jan 23 at 20:42
user6180959user6180959
112
edited Feb 8 at 4:29
user6180959
asked Jan 23 at 20:42
user6180959user6180959
112
asked Jan 23 at 20:42
user6180959user6180959
112
asked Jan 23 at 20:42
user6180959user6180959
112
112
1
$begingroup$
@Elborito 0 < x < d, I have edited the problem, please refer to the newest version :)
$endgroup$
– user6180959
Feb 8 at 4:32
add a comment |
1
$begingroup$
@Elborito 0 < x < d, I have edited the problem, please refer to the newest version :)
$endgroup$
– user6180959
Feb 8 at 4:32
1
1
$begingroup$
@Elborito 0 < x < d, I have edited the problem, please refer to the newest version :)
$endgroup$
– user6180959
Feb 8 at 4:32
$begingroup$
@Elborito 0 < x < d, I have edited the problem, please refer to the newest version :)
$endgroup$
– user6180959
Feb 8 at 4:32
add a comment |
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$begingroup$
@Elborito 0 < x < d, I have edited the problem, please refer to the newest version :)
$endgroup$
– user6180959
Feb 8 at 4:32