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 , wh**ich* *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?*

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*}$

Re: Dispersion of faultless operation and earthquake to happen

Thank you very much! Sorry for the bad translation!(Crying)