Q$1.[30$pt$]$ Availability is the most important consideration for designing servers, followed closely by scalability and throughput.

a$.[10$pt$]$ We have a single processor with a failure in time $($FIT$)$ of $3000.$ What is the mean time to failure $($MTTF$)$ for this system? Note: FIT is the number of failures per billion hours. FIT of $1$ means $1$ failure per ${10}^9$ hours.

b$.[10$pt$]$ If it takes $5$ days to get the sy$$tem running again, what is the availability of the system?

c$.[10$pt$]$ Imagine that the government, to cut costs, is going to build a supercomputer out of inexpensive computers rather than expensive, reliable computers. What is the MTTF for a system with $10,000$ processors? Assume that if one fails, the whole system fails.