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Computing an expectation

  1. Dec 4, 2013 #1
    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##?
     
  2. jcsd
  3. Dec 4, 2013 #2

    mathman

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    Science Advisor

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

    E(Si) = cE(Si-1)

    So E(Sn) = cnS0
     
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