2. (15 pts.) Assume you have a page reference string for a process running on a system with m physical pages available to the process. All of the process's pages are initially non-resident in memory. The page reference string has length p with n distinct page numbers occurring in it. The process is running uninterrupted a. For the FIFO page replacement algorithm, suppose that the reference string is given by 1, 2, 3, , n, 1, 2, 3, , n, (1 through n repeating to length p). If m-n, and p>2 * n, how many page faults will occur? Explain briefly b. For the same problem, but with m-n -1, how many page faults will occur? c. For the same problem, but with m-1, how many page faults will occur? d. For any reference string with p> n and any page replacement algorithm, what is a lower bound on the number of page faults that will occur if none of the pages are initially in memory? Explain briefly e. Is it possible for the FIFO algorithm to suffer from Belady's anomaly? f. Is pssile for the Optimal algorithm to suffer from Belady's anomaly