In an AWS Cloud System, the data center crashes once per month and it takes $($Y$)$ mins to repair and restart the data center operation. Assuming that there are $31$ days in the month and the time to repair $($Y$)$ mins is the first $3-$digits of your student$$s number. Calculate the following performance parameters of the AWS Cloud System.

a$.$ What will be the Mean Time To Fail $($MTTF$)$

b$.$ What will be the Failures In Time $($ FIT$)?$

c$.$ What is the Mean Time Between Failure $($MTBF$)?$

d$.$ What is the Availability of the system?

e$.$ What will be the Reliability of the system?