# Thread: Dispersion of faultless operation and earthquake to happen

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

I need help for these 2 tasks:
1. Let’s 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. Let’s 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?

2. ## 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*}

3. ## Re: Dispersion of faultless operation and earthquake to happen

Thank you very much! Sorry for the bad translation!