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Math Help - How many coin flips until first tail (or head)

  1. #1
    Member courteous's Avatar
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    Question How many coin flips until first tail (or head)

    1. How many coin flips are expected for the first tail?
    2. X is number of coin flips before first tail. What is X's dispersion, D(X)?
    1. \sum_{i=0}^\infty \frac{1}{2^i} = 2
    2. D(X)=E(X-E(X))^2=E(X^2)-(E(X))^2 ... but what is E(X^2)? The answer given is 2.
    Last edited by courteous; September 15th 2010 at 12:46 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'm guessing that this is a geo with p=.5.
    X is the trial in which the first heads appears?
    D would be the variance then, also known as the dispersion.
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  3. #3
    Member courteous's Avatar
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    Yes, but how do you get 2 (which is the answer) for the second point/question?
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  4. #4
    MHF Contributor matheagle's Avatar
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    The expectation of a geo is 1/p.
    That's easy to prove and I'm sure it's online too.
    It's obvious too, since the smaller p is, the longer one should wait until the the success arrives.
    Geometric distribution - Wikipedia, the free encyclopedia
    http://cnx.org/content/m13124/latest/
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  5. #5
    Member courteous's Avatar
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    Question

    1. How many coin flips are expected for the first tail?
    2. X is number of coin flips before first tail. What is D(X)?
    1. \sum_{i=0}^\infty \frac{1}{2^i} = 2 Solved this one.
    2. Don't know how to find dispersion.
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