I have the following question i am working on :
- Assume that the time it takes before a hard disk drive crashes is exponentially distributed with a mean of 5 years. Consider a RAID system consisting of 100 hard disk drives. Show that the probability that one of the disks crashes within a month is more than 80% and within a day more than 5%.
I am aware that i have to put what i have attempted but in reality i have made lots illogical attempts to solve the question but can't. I am just confused as to what lambda and t is I will appreciate an explanatory text of the different variables and how they will fit into the poisson formula
The rate is $\lambda = 100\times \dfrac 1 {5\text{ years}} = 20\text{ per year} = \dfrac{20}{12} \text{ per month} = \dfrac 5 3 \text{ per month}$.
The probability that the number of occurrences in a month is $0$ is therefore $$ \frac{(5/3)^0 e^{-5/3}}{0!} \approx 0.1888756. $$
Proceed similarly for a period of one day.