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Math Help - Central limit Theorem problem (exponential(2))

  1. #1
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    Central limit Theorem problem (exponential(2))

    Let X1,X2,... be i.i.d. with distribution Exponential(2). Use the central limit theorem to estimate the probability.

    S is a sumation 1000 = n k = 1 <= is greater or less then. (sorry I don't know latex and I can't transfer word 07 equations over)

    1000
    P(S Xn <= 505)
    k=1

    This is what i can do.

    E(x) = 1/2 var(x)= 1/4 Sd(x) = 1/2
    so,
    P( (S1000 - 1000*.5) /(sqrt(1000)*.5 ) <= (505 - 1000) /(sqrt(1000) * .5 ) )
    I don't know where to go from here nor do I know if i set the problem up correctly. Sorry about the notation and stuff I don't know how to right equations in this. If I start to come here often I will learn latex.
    Last edited by JeremyH; March 30th 2009 at 01:01 AM.
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  2. #2
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    Quote Originally Posted by JeremyH View Post
    Let X1,X2,... be i.i.d. with distribution Exponential(2). Use the central limit theorem to estimate the probability.

    S is a sumation 1000 = n k = 1 <= is greater or less then. (sorry I don't know latex and I can't transfer word 07 equations over)

    1000
    P(S Xn <= 505)
    k=1

    This is what i can do.

    E(x) = 1/2 var(x)= 1/4 Sd(x) = 1/2
    so,
    P( (S1000 - 1000*.5) /(sqrt(1000)*.5 ) <= (505 - 1000) /(sqrt(1000) * .5 ) )
    I don't know where to go from here nor do I know if i set the problem up correctly. Sorry about the notation and stuff I don't know how to right equations in this. If I start to come here often I will learn latex.
    Z_n = \frac{S_n - n \mu}{\sigma \sqrt{n}} = \frac{S_n - 500}{5 \sqrt{10}}.

    Substitute S_n = 505: Z_n = \frac{1}{\sqrt{10}} \approx 0.3162.

    So calculate \Pr(Z \leq 0.3162) where Z ~ Normal(0, 1).
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