Conditional probability and entropy: How do I interpret given data?As the title explains, I never could understand probabilities. It's one of those things that how much I try, I can't quite understand.I have to do one homework exercise about entropy and I'm given a set of probabilities. I know how to calculate entropy but I don't know how to interpret the given data.The alphabet is S={1,2} and the conditional probabilities are P(1|1)=0.8 P(2|1)=0.2 P(1|2)=0.6 P(2|2)=0.4 and P(1,2)=P(2,1)I've created this table (don't know if it is right or not): | X = 1 | X = 2 Y = 1 | 0,8 | 0,2 Y = 2 | 0,6 | 0,4I know that I need the probability of 1 and 2 to calculate the entropy. To get the probability of 1 is like this?P(1)=P(1,2)P(2|1)If so, How can I get P(1,2)?I know that P(1)=0.75 and P(2)=0.25 but I don't understand how to get to this result

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Conditional probability and entropy: How do I interpret given data?As the title explains, I never could understand probabilities. It&#039;s one of those things that how much I try, I can&#039;t quite understand.I have to do one homework exercise about entropy and I&#039;m given a set of probabilities. I know how to calculate entropy but I don&#039;t know how to interpret the given data.The alphabet is S={1,2} and the conditional probabilities are P(1|1)=0.8 P(2|1)=0.2 P(1|2)=0.6 P(2|2)=0.4 and P(1,2)=P(2,1)I&#039;ve created this table (don&#039;t know if it is right or not):       | X = 1 | X = 2 Y = 1 |  0,8  |  0,2 Y = 2 |  0,6  |  0,4I know that I need the probability of 1 and 2 to calculate the entropy. To get the probability of 1 is like this?P(1)=P(1,2)P(2|1)If so, How can I get P(1,2)?I know that P(1)=0.75 and P(2)=0.25 but I don&#039;t understand how to get to this result

Zackery Harvey · Accepted Answer

here, the explicit solution: You have,  P  (  1  )  =            P      (      1      ,      2      )              P      (      2              |            1      )      and  P  (  2  )  =            P      (      2      ,      1      )              P      (      1              |            2      )      Because ofP(2,1)=P(1,2)we get:  P  (  1  )  ∗  P  (  2      |    1  )  =  P  (  2  )  ∗  P  (  1      |    2  )  P  (  1  )  =  3  ∗  P  (  2  )Furthermore, you have P(1)+P(2)=1 and hence  4  ∗  P  (  2  )  =  1Hence  P  (  2  )  =  0.25

Conditional probability and entropy: How do I interpret given data? As the title explains, I never

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