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Chapter 9: Q. 9.12 (page 412)

Determine the entropy of the sum that is obtained when a pair of fair dice is rolled.

Short Answer

Expert verified

The entropy of the sum is H(X)-3.27when a pair of fair dice is rolled.

Step by step solution

01

Given Information

We have to find the entropy of the sum that is obtained when a pair of fair dice is rolled.

02

Simplify

We haveX鈭�2,...,12and the distribution of Xis

X~234567891011121/362/363/364/365/366/365/364/363/362/361/36

Now, the entropy will be

H(X)=-鈭�i=212pilog2pi=-鈭�j36j=15log2j36-636log2636=3.27

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