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Math Help - solve it in Poisson Theorem

  1. #1
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    Cool solve it in Poisson Theorem

    look the question ,i could'nt solve it perfectly
    my question is :how it from step 1 to step 2.and how it from step 2 to step 3?
    please help me and solve it.
    thx
    Attached Thumbnails Attached Thumbnails solve it in Poisson Theorem-part3.e1.30.gif  
    Last edited by neworld222; June 30th 2007 at 07:48 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by neworld222 View Post
    look the question ,i could'nt solve it perfectly
    I don't see a question here. Could you give some mone expalantion.

    The only thing here that I see that could need explanation is that:

    <br />
e^x = \lim_{n \to \infty} \left(1+\frac{x}{n} \right)^n<br />

    so as 100 is large (for our purposes):

    <br />
\left(1-\frac{1}{500}\right)^{100} \approx e^{-1/5}<br />

    RonL
    Last edited by CaptainBlack; June 30th 2007 at 06:27 AM.
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  3. #3
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    Cool

    Quote Originally Posted by CaptainBlack View Post
    I don't see a question here. Could you give some mone expalantion.

    The only thing here that I see that could need explanation is that:

    <br />
e^x = \lim_{n \to \infty} \left(1+\frac{x}{n} \right)^n<br />

    so as 100 is large (for our purposes):

    <br />
\left(1-\frac{1}{500}\right)^{100} \approx e^{-1/5}<br />

    RonL
    i'd update my question,please view it again
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by neworld222 View Post
    look the question ,i could'nt solve it perfectly
    my question is :how it from step 1 to step 2.and how it from step 2 to step 3?
    please help me and solve it.
    thx
    I don't understand what exactly your question is about how to go from step 2 to step 3? Just plug it into a calculator.

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    I don't understand what exactly your question is about how to go from step 2 to step 3? Just plug it into a calculator.

    -Dan
    i get subject on a book.
    there says it go from step 2 to setp 3 by 'poisson theorem'.
    i don't comprehend about 'poisson theorem'.so i need help in this math forum
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  6. #6
    Forum Admin topsquark's Avatar
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    Poisson's Theorem says:
    \frac{n!}{k!(n - k)!}p^kq^{n-k} \approx e^{-np} \frac{(np)^k}{k!}
    so this would refer to going from step 1 to step 2, not 2 to 3.

    But I don't see the applicability here. The only sensible (to me) way to approximate something like
    \left ( 1 - \frac{1}{500} \right )^{100}
    is to use the binomial approximation:
    \left ( 1 - \frac{1}{500} \right )^{100} \approx 1 - 100 \cdot 1 \cdot 1^{99} \cdot \left ( \frac{1}{500} \right ) ^{1}

    We could use Poisson's theorem on the second term and get that
    100 \cdot \left ( \frac{1}{500} \right ) ^1 \cdot 1^{99} \approx  e^{-100 \cdot \frac{1}{500}} \frac{(100 \cdot \frac{1}{500})^1}{1!} \approx 0.163746
    but this is a horrid approximation.

    -Dan
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by neworld222 View Post
    look the question ,i could'nt solve it perfectly
    my question is :how it from step 1 to step 2.and how it from step 2 to step 3?
    please help me and solve it.
    thx

    There is no use for Poisson's theorem here. I have already explained in
    another post how you get to line 2 from line 1.

    Line 3 is obtained by evaluating line 2 on your calculator.

    Poisson's theorem tell you how to approximate a binomial distribution (under
    certain conditins) by a Poisson distribution, and if that is involved in this
    question it occured before your line 1.

    RonL
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  8. #8
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    i see.if there used Poisson theory.it should be between step 1 and step 2.not 2 and 3.
    both CaptainBlack's and topsquark methods can solve this subject(lim. and Poisson theory).
    i thought they don't typeset my book's clearly,and i did'nt see the subject carefulness enough,so i thought the Poisson Theory used in the 3rd step
    now i have understand how y works to step 3.
    thx all of you.
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