Find the probability distribution of x

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Golomb examples:-

Construct the Golomb codes for the following numbers using the indicated value of b: (28, b = 2), (203, b = 32).

Gamma codes*:-

Let x be a positive integer. The γ code for x consists of a unary code for 1 + log x followed by the binary code for x - 2log x.

Essentially, the first part of the γ code tells how many bits are required to code x in binary, and the second part is the binary code for x with all bits preceding the second 1 omitted. For example, the γ code for 13 is 1110 followed by 101, indicating the binary code 1101 of length 4.

(a) Find the γ code for 20.

(b) The length of the gamma code is approximately 1+2 log x bits.

Find the probability distribution of x that would make the γ code the one minimizing average length.

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