Mixing
Define “Canonical Outcome Space” in plain English
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I'm trying to grasp what the below author is intending by "canonical outcome space", but I'm not quite sure what she is referring to, especially with her phrasing. If someone can offer a plain English explanation or explicate what she's already said, that would be super helpful!
Where I'm having difficulty:
Given $$chi= { X_1,X_2,...,X_n}$$
and an assignment $$X_1=x_1, X_2=x_2,...,X_n=x_n$$
is it such that $$
Values(X_i) = {x_1,x_2,...,x_n}, iin{1,2,...,n}$$
Meaning $X_1=x_1$, or we can have $X_1=x_2$ and so on until $X_1=x_n$ as possible values for each $X_i$
or is it that
$$ Values(X_i) = { x_i }, iin{1,2,...,n}$$ which is to say only one assignment is possible for each $X_i$?
What trips me up is
...for a choice of values $x_1,...,x_n$ for all variables. Moreover,any two such events must be either identical or disjoint, since they both assign values to all the variables in $chi$
and what KO's me is this
In addition, any event defined using variables in $chi$ must be a union of a set of such events.
If someone can break this down for me/fill in the gaps, much thanks!
probability probability-theory probability-distributions
asked Jan 17 at 5:21
Matt1991Matt1991
586
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add a comment |
$begingroup$
I'm trying to grasp what the below author is intending by "canonical outcome space", but I'm not quite sure what she is referring to, especially with her phrasing. If someone can offer a plain English explanation or explicate what she's already said, that would be super helpful!
Where I'm having difficulty:
Given $$chi= { X_1,X_2,...,X_n}$$
and an assignment $$X_1=x_1, X_2=x_2,...,X_n=x_n$$
is it such that $$
Values(X_i) = {x_1,x_2,...,x_n}, iin{1,2,...,n}$$
Meaning $X_1=x_1$, or we can have $X_1=x_2$ and so on until $X_1=x_n$ as possible values for each $X_i$
or is it that
$$ Values(X_i) = { x_i }, iin{1,2,...,n}$$ which is to say only one assignment is possible for each $X_i$?
What trips me up is
...for a choice of values $x_1,...,x_n$ for all variables. Moreover,any two such events must be either identical or disjoint, since they both assign values to all the variables in $chi$
and what KO's me is this
In addition, any event defined using variables in $chi$ must be a union of a set of such events.
If someone can break this down for me/fill in the gaps, much thanks!
probability probability-theory probability-distributions
asked Jan 17 at 5:21
Matt1991Matt1991
586
$endgroup$
add a comment |
$begingroup$
I'm trying to grasp what the below author is intending by "canonical outcome space", but I'm not quite sure what she is referring to, especially with her phrasing. If someone can offer a plain English explanation or explicate what she's already said, that would be super helpful!
Where I'm having difficulty:
Given $$chi= { X_1,X_2,...,X_n}$$
and an assignment $$X_1=x_1, X_2=x_2,...,X_n=x_n$$
is it such that $$
Values(X_i) = {x_1,x_2,...,x_n}, iin{1,2,...,n}$$
Meaning $X_1=x_1$, or we can have $X_1=x_2$ and so on until $X_1=x_n$ as possible values for each $X_i$
or is it that
$$ Values(X_i) = { x_i }, iin{1,2,...,n}$$ which is to say only one assignment is possible for each $X_i$?
What trips me up is
...for a choice of values $x_1,...,x_n$ for all variables. Moreover,any two such events must be either identical or disjoint, since they both assign values to all the variables in $chi$
and what KO's me is this
In addition, any event defined using variables in $chi$ must be a union of a set of such events.
If someone can break this down for me/fill in the gaps, much thanks!
probability probability-theory probability-distributions
asked Jan 17 at 5:21
Matt1991Matt1991
586
$endgroup$
I'm trying to grasp what the below author is intending by "canonical outcome space", but I'm not quite sure what she is referring to, especially with her phrasing. If someone can offer a plain English explanation or explicate what she's already said, that would be super helpful!
Where I'm having difficulty:
Given $$chi= { X_1,X_2,...,X_n}$$
and an assignment $$X_1=x_1, X_2=x_2,...,X_n=x_n$$
is it such that $$
Values(X_i) = {x_1,x_2,...,x_n}, iin{1,2,...,n}$$
Meaning $X_1=x_1$, or we can have $X_1=x_2$ and so on until $X_1=x_n$ as possible values for each $X_i$
or is it that
$$ Values(X_i) = { x_i }, iin{1,2,...,n}$$ which is to say only one assignment is possible for each $X_i$?
What trips me up is
...for a choice of values $x_1,...,x_n$ for all variables. Moreover,any two such events must be either identical or disjoint, since they both assign values to all the variables in $chi$
and what KO's me is this
In addition, any event defined using variables in $chi$ must be a union of a set of such events.
If someone can break this down for me/fill in the gaps, much thanks!
probability probability-theory probability-distributions
probability probability-theory probability-distributions
asked Jan 17 at 5:21
Matt1991Matt1991
586
asked Jan 17 at 5:21
Matt1991Matt1991
586
asked Jan 17 at 5:21
Matt1991Matt1991
586
asked Jan 17 at 5:21
Matt1991Matt1991
586
asked Jan 17 at 5:21
Matt1991Matt1991
586
586
add a comment |
add a comment |
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