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A channel with input x and output y has transition probability matrix:

1113_d9e846fa-b90a-43ff-8cd7-2d906a1564d6.png

Assuming an input distribution of the form

1659_e6c9ec3b-da24-4931-a3f9-6ed228886c45.png

write down the entropy of the output, H(Y ), and the conditional entropy of the output given the input, H(Y |X).

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