Suppose R = 3, 2, 4, 3, 4, 2, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 5, 6, 7, 2, 1 is a page reference stream.

a. Given a page frame allocation of 3 and assuming the primary memory is initially unloaded, how many page faults will the given reference stream incur under Belady’s optimal algorithm?

b. Given a page frame allocation of 3 and assuming the primary memory is initially unloaded, how many page faults will the given reference stream incur under LRU?

c. Given a page frame allocation of 3 and assuming the primary memory is initially unloaded, how many page faults will the given reference stream incur under FIFO?

d. Given a window size of 6 and assuming the primary memory is initially unloaded, how many page faults will the given reference stream incur under the working-set algorithm?

e. Given a window size of 6 and assuming the primary memory is initially unloaded, what is the working-set size under the given reference stream after the entire stream has been processed?