Describing Random Signals 0 I I Figure 17.1: Example of sample functiurls 2 , t 6 Under certain pre-conditions, that we will deal with later in niorc dctail, the enscnible average
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0
I
I
Figure 17.1: Example of sample functiurls 2 , ( t )
6 Under certain pre-conditions, that we will deal with later in niorc dctail, the enscnible average can also be expressed by the time-average for a sample function
approximate expected value:
6 Fkom howledge of the process, which is the complete symirictry of the die,
expectcd v:tlur is:
= 3.5 *
14-2 + 3 + 4 + 5 + 6
6
E { z ( t ) } =
As the die's syrrirrietry does riot change, the expected valiie i s the same for any time t
e If wc repeat the procedure with ~ n a n y dice whose syrnrnetxy properties we
do riot know precisely, wc can also approximately calculate the eiisenible
average by averaging all of the iiurrhm on tlie die's faces As the expected values can in general change over time, we should take the ensemble Iiiean for all dice at, the sairie time