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) Calculate the probability of a seek of length j when the head is currently positioned over track t. (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 K, for an arbitrary current position of the head. (Hint: This involves the summing over all possible combinations of movements of K tracks.) c) Calculate the average number of tracks traversed by a seek, using the formula for expected value E[x] = Si=0N-1 i Pr[x = i]. (Hint: Use the equalities Si=1n = n(n+1)/2; Si=1n i 2 = n(n+1)(2n+1)/6. d) Show that for large values of N, the average number of tracks traversed by a seek approaches N/3. explain me this