Consider a disk with N tracks numbered from 0 to (N - 1) 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. First, calculate the probability of a seek of length j when the head is currently positioned over track t.
b. Next, calculate the probability of a seek of length K.
c. Calculate the average number of tracks traversed by a seek, using the formula for expected value

d. Show that for large values of N, the average number of tracks traversed by a seek approaches N/3.

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N-1 E[x] = Eix Pr[x = i] i-0