  The paper considers truncation errors for functions of the form
$f(x_1,x_2,\dots)=g(\sum_{j=1}^\infty x_j\,\xi_j)$, i.e., errors of
approximating $f$ by $f_k(x_1,\dots,x_k)=g(\sum_{j=1}^k x_j\,\xi_j)$, where the
numbers $\xi_j$ converge to zero sufficiently fast and $x_j$'s are i.i.d.
random variables. As explained in the introduction, functions $f$ of the form
above appear in a number of important applications. To have positive results
for possibly large classes of such functions, the paper provides sharp bounds
on truncation errors in both the average and worst case settings. In the former
case, the functions $g$ are from a Hilbert space $G$ endowed with a zero mean
probability measure with a given covariance kernel. In the latter case, the
functions $g$ are from a reproducing kernel Hilbert space, or a space of
functions satisfying a H\"older condition.
