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Unformatted text preview: SES 81 an amount of time. Suppose each trial takes h time units to perform. A timescaled 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 timescaled sample
path of the timescaled 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 timescaled 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.
 Spring '08
 Zahrn
 The Land

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