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Chapter 9: Q. 9.15 (page 413)

A coin having probability p = 2 3 of coming up heads is flipped 6 times. Compute the entropy of the outcome of this experiment.

Short Answer

Expert verified

The entropy of the outcome of this experiment isHX=5.5098.

Step by step solution

01

Given Information

We have given the probability of the coinp=23.

02

Simplify

Considering random vector X=X1,鈥�,X6where Xiare independent equally distributed variables with distribution which given as

Xi~Bern23

Calculating the entropy of X.

localid="1648135034976" HX=鈭�鈭�x鈭�0,16pxlogpx

This sum contains 26summands. Then,

localid="1648135254966" 鈭�x鈭�0,16=pxlogpx=-60136log136=鈭�6113523log13516=鈭�66236log236

Hence,

HX=5.5098

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