Consider a disk with N tracks numbered from 0 to ( ) and assume that requested sectors are…

Consider a disk with N tracks numbered from 0 to () and assume that requested sectors are distributed randomly and evenly over the disk. We want to calculate the average number of tracks traversed by a seek.

a. Calculate the probability of a seek of length  when the head is currently positioned over track  (Hint: This is a matter of determining the total number of combinations, recognizing that all track positions for the destination of the seek are equally likely.)

b. Calculate the probability of a seek of length  for an arbitrary current position of the head. (Hint: This involves the summing over all possible combinations of movements of  tracks.)

c. Calculate the average number of tracks traversed by a seek, using the formula for expected value

d. Show that for large values of  the average number of tracks traversed by a seek approaches

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