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Math Help - Using Weak law of Large numbers

  1. #1
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    Using Weak law of Large numbers

    Hello,
    To give a brief background
    in my college math course on probability and statistics, the professor just finished going over Markov's inequality, Chebychev's inequality, and the Weak law of large numbers.

    I tried to figure this problem out for hours, but couldn't understand it. It is for a homework that has already been turned in (ie, this is not for a grade), but I desperately want to know the answer + explanation.

    the problem is in the attachment

    Any help will be much appreciated!
    Attached Thumbnails Attached Thumbnails Using Weak law of Large numbers-johnscan11.jpg  
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by johnj77 View Post
    Hello,
    To give a brief background
    in my college math course on probability and statistics, the professor just finished going over Markov's inequality, Chebychev's inequality, and the Weak law of large numbers.

    I tried to figure this problem out for hours, but couldn't understand it. It is for a homework that has already been turned in (ie, this is not for a grade), but I desperately want to know the answer + explanation.

    the problem is in the attachment

    Any help will be much appreciated!
    if i remember it well, \frac{1}{n} \sum_{i=1}^n X_i as n \rightarrow \infty estimates the area of the function Y_i = g(X_i) \, \forall i=1,...,n
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  3. #3
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    Quote Originally Posted by johnj77 View Post
    Hello,
    To give a brief background
    in my college math course on probability and statistics, the professor just finished going over Markov's inequality, Chebychev's inequality, and the Weak law of large numbers.

    I tried to figure this problem out for hours, but couldn't understand it. It is for a homework that has already been turned in (ie, this is not for a grade), but I desperately want to know the answer + explanation.

    the problem is in the attachment

    Any help will be much appreciated!
    The X_i's are independent identicaly distributed so:

    \lim_{N \to \infty} \frac{1}{N}\sum_{i=1}^NX_i = \bar{X}

    with probability 1.

    Also \bar{X}=1/2

    RonL
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  4. #4
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    I'm sorry, my math in this area is still weak. Captain Black, could you offer a more detailed
    explanation? In the problem what does P(Xi > x)= e^(-2x) have to do with anything? how did you get

    <br />
\bar{X}=1/2<br />
?

    (also, sorry about double posting earlier, I shouldn't have done that)
    Last edited by CaptainBlack; November 28th 2007 at 11:33 AM.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by johnj77 View Post
    I'm sorry, my math in this area is still weak. Captain Black, could you offer a more detailed
    explanation? In the problem what does P(Xi > x)= e^(-2x) have to do with anything? how did you get
    It is the complementary cumulative distribution of the X's. It is used to find
    the pdf for the X's which is used to find the mean:

    <br />
\bar{X}=1/2<br />
?

    (also, sorry about double posting earlier, I shouldn't have done that)
    RonL
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