Question: $01$ Consider the System Availability $($A$)$ of a server cluster in terms of three parameters: namely the mean time to failure $($MTTF$),$ the mean time to repair $($MTTR$),$ and a regular maintenance time $($RMT$).$ The MTTF reflects the average uptime between two adjacent natural failures. The MTTR is the downtime due to natural failure. The RMT refers to scheduled down time for hardware$/$software maintenance or updates.

a$)$ Given a cloud system with a demanded availability $\backslash (\backslash$mathrm$\{$A$\}=98\backslash \%\backslash ).$ If the MTTF is known to be two years $($or $\backslash (365\backslash$times $24\backslash$times $2=17,520\backslash )$ hours$)$ and the MTTR is known $24$ hours, what is the value of RMT in hours per month that you can schedule for this cloud system?