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Unformatted text preview: SES 81 an amount of time. Suppose each trial takes h time units to perform. A time-scaled Bernoulli random process tracks the number of counts versus time. See Figure 3.7. Figure 3.7(a) shows a (a) C’s 3 2 X’s 1 k 0 10 L1 S1 20 L2 30 S2 50 4 5 S3 ~ N (b) 3 2 40 L3 t h 1 t 0 ~ U1 ~ T 1 1 ~ U 2 2 ~ T 2 3 ~ U 3 ~ T 3 Figure 3.7: (a) A sample path of a Bernoulli process and (b) the associated time-scaled sample path of the time-scaled Bernoulli process, for h = 0.1. Bernoulli process, along with the associated random variables deﬁned in Section 2.6: the number of additional trials needed for each additional outcome of a one (the L’s), the total number of trials needed for a given number of ones (the S ’s), and the cumulative number of ones for a given number of trials (the C ’s). Note that the index in the sketch is k , which indexes the trials, beginning with trial one. Figure 3.7(b) shows the corresponding time-scaled Bernoulli process for h = 0.1. The seventh trial is the ﬁrst trial...
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## This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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