Selfinformation - Examples

Examples

  • On tossing a coin, the chance of 'tail' is 0.5. When it is proclaimed that indeed 'tail' occurred, this amounts to
I('tail') = log2 (1/0.5) = log2 2 = 1 bits of information.
  • When throwing a fair die, the probability of 'four' is 1/6. When it is proclaimed that 'four' has been thrown, the amount of self-information is
I('four') = log2 (1/(1/6)) = log2 (6) = 2.585 bits.
  • When, independently, two dice are thrown, the amount of information associated with {throw 1 = 'two' & throw 2 = 'four'} equals
I('throw 1 is two & throw 2 is four') = log2 (1/P(throw 1 = 'two' & throw 2 = 'four')) = log2 (1/(1/36)) = log2 (36) = 5.170 bits.
This outcome equals the sum of the individual amounts of self-information associated with {throw 1 = 'two'} and {throw 2 = 'four'}; namely 2.585 + 2.585 = 5.170 bits.
  • In the same two dice situation we can also consider the information present in the statement "The sum of the two dice is five"
I('The sum of throws 1 and 2 is five') = log2 (1/P('throw 1 and 2 sum to five')) = log2 (1/(4/36)) = 3.17 bits. The (4/36) is because there are four ways out of 36 possible to sum two dice to 5. This shows how more complex or ambiguous events can still carry information.

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Famous quotes containing the word examples:

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