Addition of correlated probabilities?
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Consider a set of random variables $X,Y,Z$. The random variables represent different measurements of an observable $O$ which can e.g., take on three different values $Oin{1,0,-1}$. The measurements $X,Y,Z$ have probabilities $p(X),p(Y),p(Z)$ respectively to correctly measure the current state of observable $O$. However, the measurements $X,Y,Z$ are not completely independent and their outcomes have non zero correlations $r(X,Y), r(X,Z), r(Y,Z)$. Knowing these correlations, I wonder how to calculate the joint probability for $O$ to be in state $1,0$ or $-1$ given a simultaneous measurement ${x,y,z}in {X,Y,Z}$?
I suspect that this question has an elementary answer in probability theory, but unfortunately I'm sufficiently unfamiliar with the subject so I don't know what to google for. Any explanation or referral to an external resource is much appreciated!
probability probability-theory conditional-probability correlation
asked Nov 18 at 17:03
Kagaratsch
987516
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up vote
0
down vote
favorite
Consider a set of random variables $X,Y,Z$. The random variables represent different measurements of an observable $O$ which can e.g., take on three different values $Oin{1,0,-1}$. The measurements $X,Y,Z$ have probabilities $p(X),p(Y),p(Z)$ respectively to correctly measure the current state of observable $O$. However, the measurements $X,Y,Z$ are not completely independent and their outcomes have non zero correlations $r(X,Y), r(X,Z), r(Y,Z)$. Knowing these correlations, I wonder how to calculate the joint probability for $O$ to be in state $1,0$ or $-1$ given a simultaneous measurement ${x,y,z}in {X,Y,Z}$?
I suspect that this question has an elementary answer in probability theory, but unfortunately I'm sufficiently unfamiliar with the subject so I don't know what to google for. Any explanation or referral to an external resource is much appreciated!
probability probability-theory conditional-probability correlation
asked Nov 18 at 17:03
Kagaratsch
987516
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Consider a set of random variables $X,Y,Z$. The random variables represent different measurements of an observable $O$ which can e.g., take on three different values $Oin{1,0,-1}$. The measurements $X,Y,Z$ have probabilities $p(X),p(Y),p(Z)$ respectively to correctly measure the current state of observable $O$. However, the measurements $X,Y,Z$ are not completely independent and their outcomes have non zero correlations $r(X,Y), r(X,Z), r(Y,Z)$. Knowing these correlations, I wonder how to calculate the joint probability for $O$ to be in state $1,0$ or $-1$ given a simultaneous measurement ${x,y,z}in {X,Y,Z}$?
I suspect that this question has an elementary answer in probability theory, but unfortunately I'm sufficiently unfamiliar with the subject so I don't know what to google for. Any explanation or referral to an external resource is much appreciated!
probability probability-theory conditional-probability correlation
asked Nov 18 at 17:03
Kagaratsch
987516
Consider a set of random variables $X,Y,Z$. The random variables represent different measurements of an observable $O$ which can e.g., take on three different values $Oin{1,0,-1}$. The measurements $X,Y,Z$ have probabilities $p(X),p(Y),p(Z)$ respectively to correctly measure the current state of observable $O$. However, the measurements $X,Y,Z$ are not completely independent and their outcomes have non zero correlations $r(X,Y), r(X,Z), r(Y,Z)$. Knowing these correlations, I wonder how to calculate the joint probability for $O$ to be in state $1,0$ or $-1$ given a simultaneous measurement ${x,y,z}in {X,Y,Z}$?
I suspect that this question has an elementary answer in probability theory, but unfortunately I'm sufficiently unfamiliar with the subject so I don't know what to google for. Any explanation or referral to an external resource is much appreciated!
probability probability-theory conditional-probability correlation
probability probability-theory conditional-probability correlation
asked Nov 18 at 17:03
Kagaratsch
987516
asked Nov 18 at 17:03
Kagaratsch
987516
asked Nov 18 at 17:03
Kagaratsch
987516
asked Nov 18 at 17:03
Kagaratsch
987516
asked Nov 18 at 17:03
Kagaratsch
987516
987516
add a comment |
add a comment |
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