Decimals-3

Compute the binary entropy of the following distribution of 3 probabilities:

{ $val12 , $val13 , $val14 }

Decimals-4

Compute the binary entropy of the following distribution of 4 probabilities:

{ $val13 , $val14 , $val15 , $val16 }

Decimals-5

Compute the binary entropy of the following distribution of 5 probabilities:

{ $val14 , $val15 , $val16 , $val17 , $val18 }

Given entropy - 2

Please find a distribution of probabilities on a system of two elements {A,B}, such that the binary entropy of the system is equal to $val6.

The two probabilities P(A), P(B) must be positive, and their sum must be equal to 1.


Given entropy - 3

Please find a distribution of probabilities on a system of three elements {A,B,C}, such that the binary entropy of the system is equal to $val6.

The three probabilities P(A), P(B), P(C) must be positive, and their sum must be equal to 1.


Given entropy - 4

Please find a distribution of probabilities on a system of four elements {A,B,C,D}, such that the binary entropy of the system is equal to $val6.

The four probabilities P(A), P(B), P(C), P(D) must be positive, and their sum must be equal to 1.


Existence of entropy - 3

Is there a system of 3 elements with a binary entropy equal to $val12?

Existence of entropy

Is there a system of $val6 elements with a binary entropy equal to $val13?

Computer file

A computer file weighs $val6 bytes. The content of the file only contains bytes of 4 values, as shown by the following table.

Decimal value $val17 $val18 $val19 $val20
Binary value $val21 $val22 $val23 $val24
Number of bytes $val12 $val13 $val14 $val15

Compute the binary entropy of the file, according to the numbers of bits and according to the number of bytes.


Computer file II

A computer file weighs $val6 bytes. The content of the file only contains bytes of 6 values, as shown by the following table.

Value of byte $val21 $val22 $val23 $val24 $val25 $val26
Number $val14 $val15 $val16 $val17 $val18 $val19

The binary entropy of the file is according to the numbers of bytes.

By recoding the bytes of the file by an optimal binary code of variable length, one can reduce the size of the file to bytes (without counting eventual headers).


Color image

A color image of $val6×$val7 pixels is composed of 5 colors: black, white, red, green, blue. Here is the number of pixels of each color in the image.

Color Black White Red Green Blue
Pixels $val15 $val16 $val17 $val18 $val19

Compute the binary entropy of the image according to the numbers of pixels.


Max of entropy - 3

We have a system of distribution of probabilities on 3 elements {A,B,C}. Given that the probability P(A) = $val6, what is the maximum and the minimum of the binary entropy of the system?

Max of entropy II - 3

We have a system of distribution of probabilities on 3 elements {A,B,C}. Given that the probability P($val8) = $val7 and that

P(A) $m_ge P(B) $m_ge P(C) ,

what is the maximum and the minimum of the binary entropy of the system?


Rationals-3

Compute the binary entropy of the following distribution of 3 probabilities:

{ $val16 }

Rationals-4

Compute the binary entropy of the following distribution of 4 probabilities:

{ $val20 }

Rationals-5

Compute the binary entropy of the following distribution of 5 probabilities:

{ $val20 }

Rationals-6

Compute the binary entropy of the following distribution of 6 probabilities:

{ $val22 }

Conditional existence - 3

Is there a system of 3 elements {A,B,C}, such that P(A) = $val8, and that the binary entropy is equal to $val14?

Conditional existence - 4

Is there a system of 4 elements {A,B,C,D}, such that

P(A) = $val11, P(B) = $val12,

and that the binary entropy is equal to $val18?