# 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:

In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.
Michel de Montaigne (1533–1592)

There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.
Bernard Mandeville (1670–1733)

No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.
André Breton (1896–1966)