$n$ machines in total (starting working at the same time), working time of each is i.i.d. $Exp(\lambda)$. How to calculate the expectation of the number of broken machines at time $t$? (If broken, they stay broken forever)
ps: how to calculate the fraction of time when there are at least one broken machines by time t if repeating this process for infinite times? Can I use the expected time until the $1st$ broken down here?