If the probability that a given system fails in a week is p, what is the expected lifetime of the system?
I have no clue how to approach this. I have been thinking about this for a while now. Basically I wanted to find out, if my laptop fails in a year with a low probability say 1/100, what is its expected lifetime? How do I compute the expected lifetime here? Is the data insufficient to answer this? I don't know how to approach this. I hope the question makes sense.
Best Answer
The probability that it fails on the $n$'th week is that it does not fail in $n-1$ weeks then fails. Call this $P_n=p(1-p)^{n-1}$. The expected lifetime is therefore $\sum_{n=1}^\infty n P_n$. You can take it from there...