Entropy question for 2 input 1 output system

AI Thread Summary
The discussion centers on the equality H(Y|X) = H(Z|X) in a two-input, one-output system, questioning why this holds true. The user seeks clarification on whether the condition p(Y,X) = p(Z,X) is necessary for this equality. They express difficulty in demonstrating this relationship. Ultimately, the user finds the answer to their question but suggests a more suitable title for the thread. The conversation highlights the complexities of entropy in information theory.
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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