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Thread: Dispersion of faultless operation and earthquake to happen

  1. #1
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    Dispersion of faultless operation and earthquake to happen

    I need help for these 2 tasks:
    1. Letís suppose that the duration of faultless operation ξ of one computer is following an exponential distribution ξ , which belongs to Ех (λ). You have to found the valuation of the parameter λ, if we have observations on the duration of faultless operation of 5 computers- 2,3,5,4 and 7 years. What is the expected dispersion of the duration of faultless operation?

    2. Letís suggest that a heavy earthquake is happening average once per 10 years. What is the probability in the next 30 years an earthquake to happen?
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  2. #2
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    Re: Dispersion of faultless operation and earthquake to happen

    I don't really understand what you're asking in (1)

    (2) Assume that the number of heavy earthquakes is Poisson distributed with $\lambda =\dfrac{1}{10}$

    I.e. we have an average of $\dfrac{1}{10}$ an earthquake a year, or 1 in 10 years.

    Over 30 years we expect 30 times the number of quakes as in 1 year.

    $\tilde{\lambda}=\lambda (30) = \dfrac{30}{10} = 3$

    $\begin{align*}
    &P[\text{quake in next 30 yrs}] = \\
    &1 - P[\text{0 quakes in next 30 yrs}] = \\
    &1-\dfrac{\tilde{\lambda}^0~e^{-\tilde{\lambda}}}{0!} =\\
    &1 - \dfrac{3^0e^{-3}}{0!} = \\
    &1 - e^{-3} \approx 0.95
    \end{align*}$
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  3. #3
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    Re: Dispersion of faultless operation and earthquake to happen

    Thank you very much! Sorry for the bad translation!
    Last edited by dtzoneva; Jan 26th 2019 at 11:35 AM.
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