Reference string : 7,2,7,3,2,5,3,4,6,7,7,1,5,6,1
Given that 4 page Frames and LRU page replacement policy.
Access 7 which leads Miss --- 7, empty, empty, empty ------ Hits =0 , Miss = 1
Access 2 which leads Miss --- 7, 2, empty, empty ------ Hits =0 , Miss = 2
Access 7 which leads Hit --- 7, 2, empty, empty ------ Hits =1 , Miss = 2
Access 3 which leads Miss --- 7, 2, 3, empty ------ Hits =1 , Miss = 3
Access 2 which leads Hit --- 7, 2, 3, empty ------ Hits =2 , Miss = 3
Access 5 which leads Miss --- 7, 2, 3, 5 ------ Hits =2 , Miss = 4
Access 3 which leads Hit --- 7, 2, 3, 5 ------ Hits =3 , Miss = 4
Access 4 which leads Miss --- 4, 2, 3, 5 ------ Hits =3 , Miss = 5 ( 7 is replaced with 4 by LRU algorithm )
Access 6 which leads Miss --- 4, 6, 3, 5 ------ Hits =3 , Miss = 6 ( 2 is replaced with 6 by LRU algorithm )
Access 7 which leads Miss --- 4, 6, 3, 7 ------ Hits =3 , Miss = 7 ( 5 is replaced with 7 by LRU algorithm )
Access 7 which leads Hit --- 4, 6, 3, 7 ------ Hits =4 , Miss = 7
Access 1 which leads Miss --- 4, 6, 1, 7 ------ Hits =4, Miss = 8 ( 3 is replaced with 1 by LRU algorithm )
Access 5 which leads Miss --- 5, 6, 1, 7 ------ Hits =4 , Miss = 9 ( 4 is replaced with 5 by LRU algorithm )
Access 6 which leads Hit --- 5, 6, 1, 7 ------ Hits =5 , Miss = 9
Access 1 which leads Hit --- 5, 6, 1, 7 ------ Hits =6 , Miss = 9
$\therefore Pagefault\; rate = \frac{9}{15}=0.6$