A computer disk storage device has ten concentric tracks,numbered 1, 2,…, 10 from outermost to innermost, and asingle access arm. Let pi 5 the probability that any particularrequest for data will take the arm to tracki(i 5 1,… , 10). Assume that the tracks accessed in successiveseeks are independent. Let X 5 the number of tracksover which the access arm passes during two successiverequests (excluding the track that the arm has just left, sopossible X values are x 5 0, 1, …, 9). Compute the pmfof X. [Hint: P(the arm is now on track i and X 5 j) 5P(X 5 j|arm nowon i) ? pi. After the conditionalpro bability is written in terms of p1,…, p10, by the law oftotal probability, the desired probability is obtained bysumming over i.]
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A computer disk storage device has ten concentric tracks,
numbered 1, 2,…, 10 from outermost to innermost, and a
single access arm. Let pi 5 the
request for data will take the arm to track
i(i 5 1,… , 10). Assume that the tracks accessed in successive
seeks are independent. Let X 5 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 5 0, 1, …, 9). Compute the pmf
of X. [Hint: P(the arm is now on track i and X 5 j) 5
P(X 5 j|arm 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.]
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