Simple joint probability distribution

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SUMMARY

The discussion revolves around calculating the joint probability distribution for two machines, X and Y, where X influences Y's operation. When X is activated, Y turns on with a probability of 50%. If Y turns on, it has a 25% chance of breaking. The key focus is on determining the joint probability distribution of Y turning on and breaking, as well as calculating the mutual information between these two events. The participants express difficulty in starting the calculations and seek guidance on constructing the joint probability distribution.

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  • Understanding of joint probability distributions
  • Basic knowledge of conditional probabilities
  • Familiarity with mutual information concepts
  • Ability to interpret probabilistic models
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jetlam
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Homework Statement



Let's say there are two machines, X and Y. X is connected to Y.

* If X is turned on, Y turns on 50% of the time.
* If Y turns on (through X being turned on) then it breaks 25% of the time.
* Y won't break spontaneously and it can only be turned on through X.

What is the joint probability distribution between Y turning on and Y breaking?
Considering the set of times that X turns on, what is the mutual information between Y turning on and Y breaking (how many bits)?

Thanks.

2. The attempt at a solution

I'm not really sure how to start or how to make the joint probability distribution.
 
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