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Topic: Greater?
Replies: 9   Last Post: Nov 26, 2013 5:31 PM

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mluttgens

Posts: 73
Registered: 3/3/11
Re: Greater?
Posted: Nov 25, 2013 11:14 AM
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Le lundi 25 novembre 2013 16:44:48 UTC+1, Roland Franzius a écrit :
> Am 25.11.2013 16:10, schrieb luttgma@gmail.com:
>

> > Le lundi 25 novembre 2013 14:37:17 UTC+1, Roland Franzius a �crit :
>
> >> Am 25.11.2013 12:29, schrieb luttgma@gmail.com:
>
> >>
>
> >>> What is the probability that 14.5 +/- 0.8 is greater than 13.8 +/- 0.04 ?
>
> >>

>
> >>
>
> >>
>
> >> For two random production processes X, Y, normally and stochastic
>
> >>
>
> >> independently distributed with CDF NormalDistribution(m_k,s_k), the
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> >>
>
> >> difference is normally distibuted with
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> >>
>
> >> mean = difference of the means and variance = sum of variances:
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> >>
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> >>
>
> >>
>
> >> F(z)=Pr[X-Y < z ]
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> >>
>
> >> = N( m1-m2, sqrt(s1^2+s2^2) ) = N(0.7,sqrt(0.064+0.0016) )
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> >>
>
> >> So the answer may be probably
>
> >>
>
> >>
>
> >> CDF[NormalDistribution[0.7, Sqrt[0.8^2 + 0.04^2]]][0] -> 0.191084
>
>
>

> >>
>
> >> Roland Franzius
>
> >
>
> > 14.5 +/- 0.8 billion years is the estimated age of the so-called "Methuselah star," cataloged as HD 140283.
>
> > 13.8 +/- 0.04 billion years is the estimated age of the Universe.
>
> >
>
> > According to your aanalysis, the probability that HD 140283 is older than the Universe is rather small.
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>
>
>
>
> No the other way around, swap the variables.
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>
>
> But, by the way, the statistical independency of birth of parents and
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> childs is currently not yet widespreadly assumed and the error marges in
>
> astrophysics don't describe distributions of times but statistical
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> errors in measurement procedures eg by repeated mesurements of the same
>
> variable.
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>
>
> In the preparatoy laboratory courses the question is discussed thorouhly
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> if one can estimate the the distance between the main train station and
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> Bunsen-St. only by counting steps and taking the mean of 10000 walks and
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> their variance to get a precision of 3 inches.
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>
>
>
>
> So, even if by radio carbon methods the age of bones of parents and
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> childs in an egyptian tomb dates the children before the parents with no
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> overlap, its not worth taking notice.
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>
>
>
>
>
>
> --
>
>
>
> Roland Franzius


Thank you again!

If I understand correctly, it cannot statistically be assumed that HD 140283 is older than the Universe, in spite of a probability of about 0.8

Marcel



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