# Separate chances from "joint" probability

Suppose I have a binary vector $v$ that is replicated two times by 2 different equipments $M$ and also $N$, causing 2 new vectors $x$ and also $y$.

Both equipments are damaged in the feeling that they both could fall short to replicate each personality appropriately. Extra officially, $M$ has an affiliated vector $e_M$ of size $|v|$, where $(e_M)_i$ is the probability that little bit $i$ in $M$ is input will certainly be inverted in $M$ is result (and also $N$ has actually an in a similar way specified, yet not always the same, affiliated vector $e_N$).

Inquiries:

1. if the only details I receive is $x$, $y$, and also 2 actual numbers $p$ and also $q$ defining the chances that a blunder has been made in generating $x$ and also $y$ (i.e. $p$ is the probability that $M$ made a mistake when generating $x$ from $v$, and also $q$ is the probability that $N$ made a mistake when generating $y$ from $v$), exists a means to rebuild, or approximate $e_M$ and also $e_N$?

2. does the response to inquiry 1 rely on $|v|$ (which is certainly thought to be at the very least $2$ for this inquiry to make good sense), and also if so, just how?

(all apologies if the inquiry is unimportant, and also if I'm not making use of the appropriate terms)

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2019-05-18 21:37:34
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$1-p$ offers you the item of $(1-(e_M)_i)$ over $i$ and also in a similar way for $1-q$. If you just have one set of $x$ and also $y$ and also do not recognize anything concerning the $(e_M)_i$ and also $(e_N)_i$ there is no hope. Also if you get a great deal of $x,y$ sets yet do not get any kind of details of what is the fact all you can inform is the mix of mistake prices per little bit. The opportunity of argument at an offered little bit is $e_M+e_N-e_M*e_N$ yet you can not iron out anymore than that.