A computer disk storage device has ten concentric tracks, numbered 1, 2,..., 10 from outermost to innermost, and a single access arm. Let pi = the probability that any particular request for data will take the arm to track i(i = 1,... , 10). Assume that the tracks accessed in successive seeks are independent. Let X = the number of tracks over which the access arm passes during two successive
requests (excluding the track that the arm has just left, so possible X values are x = 0, 1, ..., 9). Compute the pmf of X. [Hint: P(the arm is now on track i and X = j) = P(X = jlarm nowon i) ? pi. After the conditional pro bability is written in terms of p1,..., p10, by the law of total probability, the desired probability is obtained by summing over i.]