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Specifically, you can assume we have n random variables $X_i$ ($i \in \{1,2,3,\ldots,n\}$). Each $X_i$ has a probability $P_i$ to payoff $\mathrm{UP}_i$ and probability $Q_i=1-P_i$ to payoff $\mathrm{DOWN}_i$. $S= \sum_i X_i$. What is the probability density and cumulative distribution of $S$?

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    Are the random variables independent?2012-08-02
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    Yes, you can assume independence2012-08-02
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    The variable $S$ is a discrete random variable, based on your description. Hence, the concept of probability _density_ is not applicable. Do you mean point mass function, maybe?2012-08-02
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    Yes, of course that is what I meant.2012-08-02

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