$8\mathrm{.}4$ Consider the following string of page references $7,0,1,2,0,3,0,4,2,3,0,3,2.$ Complete a figure similar to Figure $8\mathrm{.}15,$ showing the frame allocation for:

a$.$ FIFO $($first$-$in$-$first$-$out$)$

b$.$ LRU $($least recently used$)$

d$.$ Optimal $($assume the page reference string continues with $1,2,0,1,7,0,1)$

e$.$ List the total number of page faults and the miss rate for each policy. Count page faults only after all frames have been initialized.