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 $S$?
What is the distribution of the sum of n binary random variables with different probabilities and payoffs each?
1
$\begingroup$
probability
statistics
-
0Are the random variables independent? – 2012-08-02
-
0Yes, you can assume independence – 2012-08-02
-
0The 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
-
0Yes, of course that is what I meant. – 2012-08-02