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Simple information problem

  1. Sep 21, 2007 #1

    svm

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    In some village rain falls with probability of 0.5 (statistically), e.g. tomorrow it may or may not fall, the chances are equal.

    A local meteorologist gathers information, allowing him only to predict rain falling in the village with average success rate of 75% (about 3 of 4 predictions are correct).

    What amount of information allows him to predict rain falling for a given day?
    (The information is meaningful only for this particular prediction, no other uses are possible)
     
  2. jcsd
  3. Sep 22, 2007 #2

    CRGreathouse

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    You only need 1 bit to learn it perfectly (-lg 0.5), so you're talking about fractions of a bit. I get about 0.42 bits.
     
  4. Sep 22, 2007 #3

    svm

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    Hm... That's interesting. My answer was only about 0.19 bit:
    1 - (- 0.75 * lg 0.75 - 0.25 * lg 0.25) bit

    Am I wrong?
     
  5. Sep 22, 2007 #4

    CRGreathouse

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    You're right, I wasn't answering your question. I was saying how much information there was in the 75% prediction total. (Sorry!)
     
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