Problem 1: Process management and evaluating system performancea) A RAM of a computer system is sufficient to store in full five application programs. Each of those programs is idle (due to waiting for I/O) for 50% of the time. Assuming optimal scheduling of these programs by the OS, and that the underlying hardware has a single CPU, what fraction (%) of the CPU time will be wasted on average? (Simplifying assumption: wasted time by CPU is considered to be any time that CPU is not executing one of those five programs. Assume also, no other programs are being swapped into RAM.) b) Consider a multi-programmed system with six programs in RAM at the same time. Assume each process corresponds to one of those six programs in execution, and each process spends 40% of time waiting for I/O. What will be the CPU utilization? (Again, assume just a single processor.)(Hint: You need a basic probability theory to answer this one. Assume, in both parts, that exactly when is each process idle are independent, identically distributed random variables.)