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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. Lei 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 probability is written in terms of p1,…, p10, by the law of total probability, the desired probability is obtained by summing over i.]
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Probability and Statistics for Engineering and the Sciences
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