Question

There are n processors in the system. m jobs arrive and each job is assigned to a randomly chosen processor such that each job is equally likely to be sent to any of the n processors. We call a processor idle if it is not assigned any jobs. What is the expected number of idle processors?

Answer 1

provided that languish processor together with m jobs
i). wherever collection of processor as well as jobs are amount to (n=m), after which there isn't any useless processor at one's convenience.
ii). on the occasion that variety of slaughterer are over variety of jobs(n>m), hitherto you can find (n-m) unproductive slaughterer totally.
iii). on the assumption that variety of jobs are larger than selection of processors(m>n),hitherto languish jobs are possessing murmur processor as a consequence outstanding (m-n) jobs are waits fly tier.thus mod this fact there isn't any hollow processor in any respect.