TITLE: Computing probabilities for sums of random variables
QUESTION [0 upvotes]: Let $p$ be some probability and let $X_i$ be random variables such that $X_i = x_i$ with probability $p$ and $X_i = 0$ otherwise, where $x_i$ are fixed positive constants, for $i=1,...,n$.
If I fix some probability $\pi$, how do I efficiently compute $c$ in the following equation?
$$P\left(\sum X_i < c\right)\geq\pi$$
Thanks, much appreciated.

REPLY [0 votes]: An easy way to do this is to set $c=1+\sum x_i$, then 
$$
P\left(\sum X_i<c\right)=1 \geq \pi
$$
for all possible probability value given to $\pi$.
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