Drive an expression for average distance moved by a head from one cylinder to another (in terms of the number of head movements). Movements are made at random and the disk has N concentric cylinders numbered from 0 to N-1 with the innermost cylinder numbered 0. Assume that when seeking the next cylinder, all cylinders have an equal probability of being selected. Show that the average movement approaches N/3 for large values of N. Hint: Consider the Kth cylinder and calculate the number of steps needed to move to the 7th cylinder where /varies from 0 to (N 1).