What is the Expected Value in a Probabilistic Computing Scenario?

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    Computing Expectation
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SUMMARY

The expected value in a probabilistic computing scenario is calculated using the formula E(Sn) = cnS0, where c is defined as c = p(1+b) + (1-p)(1+a). This formula derives from the recursive relationship E(Si) = cE(Si-1), indicating how the expected value evolves over n iterations. The discussion emphasizes the importance of understanding the probabilities p, and the constants a and b in determining the expected outcome.

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Assume we have a number ##S_0##. For ##i=1..n## define$$S_i=\begin{cases}(1+b)S_{i-1}\text{ with probability }p\\(1+a)S_{i-1}\text{ with probability }1-p\end{cases}$$.
What is the expected value of ##S_n##?
 
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Let c = p(1+b) + (1-p)(1+a)

E(Si) = cE(Si-1)

So E(Sn) = cnS0
 

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