Suppose I have $k$ random variables $X_i, i=1,2,...,k$ sampled independently from a certain distribution with expectation $\mu$ and variance $\sigma^2$. Now I compute $C$ as follow:
Initially $C=0$, at each round $i$, $C \leftarrow \max(C+X_i, 0)$
Now After $k$ rounds of computation, what is $C$'s expectation and variance? How can I measure it?
If I can't measure it exactly, what is the empirical error for C compare with the expectation of ($\sum^k_i X_i$).