Exercise #1:

Optimal:

r | 0  1  7  2  0  3  1  7  0  1  7  
------------------------------------
0 | 0  0  0  0  0  0  0  0  0  0  0 
1 | -  1  1  1  1  1  1  1  1  1  1
2 | -  -  7  7  7  7  7  7  7  7  7
3 | -  -  -  2  2  3  3  3  3  3  3 
------------------------------------
f | X  X  X  X  -  X  -  -  -  -  - 

(5 page faults)


FIFO:

r | 0  1  7  2  0  3  1  7  0  1  7
------------------------------------
0 | 0  0  0  0  0  3  3  3  3  3  3 
1 | -  1  1  1  1  1  1  1  0  0  0 
2 | -  -  7  7  7  7  7  7  7  1  1 
3 | -  -  -  2  2  2  2  2  2  2  7 
------------------------------------
f | X  X  X  X  -  X  -  -  X  X  X

(8 page faults)


LRU:

r | 0  1  7  2  0  3  1  7  0  1  7 
------------------------------------
0 | 0  0  0  0  0  0  0  0  0  0  0 
1 | -  1  1  1  1  3  3  3  3  3  3 
2 | -  -  7  7  7  7  1  1  1  1  1 
3 | -  -  -  2  2  2  2  7  7  7  7 
------------------------------------
f | X  X  X  X  -  X  X  X  -  -  -

(7 page faults)

------------------------------------

Exercise #3:

	Let d be the probability of a page being dirty. We have:

	400ns = 100ns + 0.00003 * ( (1 - d) * 6ms  + d * 12ms)

	we have 1ms = 10^6 ns, so putting everything in ns, we need to solve

        300 = 0.00003 * ((1 - d) * 6000000 + d * 12000000)


        or 

        d = (300/0.00003 - 6000000) / 6000000 = 2/3

	this is: pages are dirty 66% of the time