Assuming $n$ independent random variables $g_i \in \lbrace0,1\rbrace$,
which takes the value 1 with probability of $p_i$.
Asumming $x_i\in\mathbb{R}$ , how can I calculate the following expectation ?
$$ E_{g_i} [\max (0, \sum_{i=1}^n x_ig_i)]$$
Is it possible to approximate or to bound the above with the Poisson destitution? what will be the $\lambda$ in such case ?