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A computer disk storage device has ten concentric tracks,
Chapter 4, Problem 117E(choose chapter or problem)
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 . Assume that the tracksi(i = 1, ………,10) 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 = j|arm now on i).p.i 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.]
Questions & Answers
QUESTION:
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 . Assume that the tracksi(i = 1, ………,10) 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 = j|arm now on i).p.i 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.]
ANSWER:Answer : Step 1 : Given 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. We assume that t