Suppose I have a binary vector $v$ that is copied twice by two separate machines $M$ and $N$, resulting in two new vectors $x$ and $y$.
Both machines are faulty in the sense that they both might fail to copy each character correctly. More formally, $M$ has an associated vector $e_M$ of length $|v|$, where $(e_M)_i$ is the probability that bit $i$ in $M$'s input will be inverted in $M$'s output (and $N$ has a similarly defined, but not necessarily identical, associated vector $e_N$).
if the only information I receive is $x$, $y$, and two real numbers $p$ and $q$ describing the probabilities that a mistake has been made in producing $x$ and $y$ (i.e. $p$ is the probability that $M$ made an error when producing $x$ from $v$, and $q$ is the probability that $N$ made an error when producing $y$ from $v$), is there a way to reconstruct, or approximate $e_M$ and $e_N$?
does the answer to question 1 depend on $|v|$ (which is of course assumed to be at least $2$ for this question to make sense), and if so, how?
(all apologies if the question is trivial, and if I'm not using the right terms)