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Math Help - Strong Law of Large Numbers

  1. #1
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    Strong Law of Large Numbers

    The distribution function F(z) =

    {0 if z< 5
    {z/10 if 5 <= z < 8
    {1-e^(-z/8) if 8 <= z

    is associated with the MPG of a car. Using the Strong Law of Large Numbers, what may be the MPG?

    Where should I start this problem and how would I go about using the Strong Law of Large Numbers? Would the expected cost be E(|z-beta|)? Any help would be appreciated
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'm not sure what beta is here.
    BUT all I think they want you to do is compute the expected MPG.
    The sample mean converges to this population mean is the point.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    I'm not sure what beta is here.
    BUT all I think they want you to do is compute the expected MPG.
    The sample mean converges to this population mean is the point.
    with the function provided, how do I compute the expected MPG? Can you provide an example?
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  4. #4
    MHF Contributor matheagle's Avatar
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    f(z)=.1 on 5\le z <8

    and

    f(z)= {1\over 8}e^{-z/8} on  z \ge 8

    SO E(Z)=.1\int_5^8 zdz + {1\over 8}\int_8^{\infty} ze^{-z/8}dz

    HOWEVER I don't think this is a valid distribution function.
    There are jumps and it seems to be a continuous setting.
    So something is off.
    Last edited by matheagle; November 11th 2009 at 07:05 AM.
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