Entropy question for 2 input 1 output system

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SUMMARY

The discussion centers on the equality H(Y|X) = H(Z|X) in the context of a two-input, one-output system. The user seeks clarification on why this equality holds, specifically questioning the condition that p(Y,X) must equal p(Z,X). The conclusion reached is that understanding the definition of entropy is crucial to grasping this relationship. The user ultimately finds the answer to their question, indicating that the equality is valid under certain conditions.

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perplexabot
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Hey all. I have a question regarding the solution to a question, both shown below (only part of the solution is shown). Specifically the line that states: H(Y|X) = H(Z|X). Why does this equality hold? Expanding and using the definition of entropy, I can see that for the above equality to hold, p(Y,X) must equal p(Z,X), right? I am not able to show this. Please some help will be greatly appreciated.

Here is the question with part of the solution:
2015-05-25-222302_1366x768_scrot.png
 
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Hey again! I found the answer to my question, here it is:
temp_ans.png


PS: Maybe a better name for this thread would have been "Entropy of sum question." I would have renamed it if I could.
Thanks for reading.
 

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