  Given $n$ independent random variables $X_1, X_2, ..., X_n$ and an integer
$C$, we study the fundamental problem of computing the probability that the sum
$X=X_1+X_2+...+X_n$ is at most $C$. We assume that each random variable $X_i$
is implicitly given by an oracle which, given an input value $k$, returns the
probability $X_i\leq k$. We give the first deterministic fully polynomial-time
approximation scheme (FPTAS) to estimate the probability up to a relative error
of $1\pm \epsilon$. Our algorithm is based on the idea developed for
approximately counting knapsack solutions in [Gopalan et al. FOCS11].
