What is the Expected Value in a Probabilistic Computing Scenario?

[TaPaKaH]

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 $S_n$?

 

[mathman]

Let c = p(1+b) + (1-p)(1+a)

E(S_i) = cE(S_i-1)

So E(S_n) = cⁿS₀