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Determine the entropy of a source with probabilities 2/3，2/9，2/27，2/81，2/243，1/243

Determine the entropy of a source with probabilities 2/3，2/9，2/27，2/81，2/243，1/243

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Answer #1

Assuming the X values are 1, 2, 3, 4, 5, 6, the required entropy is

which can be found from the table below:

X p(X) -Xln(P(X))
1 0.666667 0.176091
2 0.222222 1.306425
3 0.074074 3.391001
4 0.024691 6.42982
5 0.00823 10.42288
6 0.004115 14.31364

Taking the sum, we have entropy as:

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