Mixing
What is the sample space in conditional probability?
1
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In conditional probabilities, the sample space at every step is dependent on previous outcomes. How do we then define a sample space? In particular, why is it possible to define the sample space of, for example, Polya's urn model as $Omega = {[B,W]}^n$ when every sequence of black and white isn't equally likely?
probability probability-theory conditional-probability polya-urn-model
asked Jan 29 at 22:55
Dis-integratingDis-integrating
1,043526
$endgroup$
add a comment |
1
$begingroup$
In conditional probabilities, the sample space at every step is dependent on previous outcomes. How do we then define a sample space? In particular, why is it possible to define the sample space of, for example, Polya's urn model as $Omega = {[B,W]}^n$ when every sequence of black and white isn't equally likely?
probability probability-theory conditional-probability polya-urn-model
asked Jan 29 at 22:55
Dis-integratingDis-integrating
1,043526
$endgroup$
2
$begingroup$
You can have a sample space in which all outcomes are not equally likely. Who says you cannot?
$endgroup$
– David K
Jan 29 at 23:12
$begingroup$
then how do you define probability in any meaningful way?
$endgroup$
– Dis-integrating
Jan 29 at 23:22
2
$begingroup$
A sample space is a set of outcomes. There is no requirement for those outcomes to be equally probable (and indeed that is why a probability space includes a probability function in its structure).
$endgroup$
– Graham Kemp
Jan 29 at 23:22
$begingroup$
thanks, makes sense
$endgroup$
– Dis-integrating
Jan 29 at 23:23
add a comment |
1
1
1
$begingroup$
In conditional probabilities, the sample space at every step is dependent on previous outcomes. How do we then define a sample space? In particular, why is it possible to define the sample space of, for example, Polya's urn model as $Omega = {[B,W]}^n$ when every sequence of black and white isn't equally likely?
probability probability-theory conditional-probability polya-urn-model
asked Jan 29 at 22:55
Dis-integratingDis-integrating
1,043526
$endgroup$
In conditional probabilities, the sample space at every step is dependent on previous outcomes. How do we then define a sample space? In particular, why is it possible to define the sample space of, for example, Polya's urn model as $Omega = {[B,W]}^n$ when every sequence of black and white isn't equally likely?
probability probability-theory conditional-probability polya-urn-model
probability probability-theory conditional-probability polya-urn-model
asked Jan 29 at 22:55
Dis-integratingDis-integrating
1,043526
asked Jan 29 at 22:55
Dis-integratingDis-integrating
1,043526
asked Jan 29 at 22:55
Dis-integratingDis-integrating
1,043526
asked Jan 29 at 22:55
Dis-integratingDis-integrating
1,043526
asked Jan 29 at 22:55
Dis-integratingDis-integrating
1,043526
1,043526
2
$begingroup$
You can have a sample space in which all outcomes are not equally likely. Who says you cannot?
$endgroup$
– David K
Jan 29 at 23:12
$begingroup$
then how do you define probability in any meaningful way?
$endgroup$
– Dis-integrating
Jan 29 at 23:22
2
$begingroup$
A sample space is a set of outcomes. There is no requirement for those outcomes to be equally probable (and indeed that is why a probability space includes a probability function in its structure).
$endgroup$
– Graham Kemp
Jan 29 at 23:22
$begingroup$
thanks, makes sense
$endgroup$
– Dis-integrating
Jan 29 at 23:23
add a comment |
2
$begingroup$
You can have a sample space in which all outcomes are not equally likely. Who says you cannot?
$endgroup$
– David K
Jan 29 at 23:12
$begingroup$
then how do you define probability in any meaningful way?
$endgroup$
– Dis-integrating
Jan 29 at 23:22
2
$begingroup$
A sample space is a set of outcomes. There is no requirement for those outcomes to be equally probable (and indeed that is why a probability space includes a probability function in its structure).
$endgroup$
– Graham Kemp
Jan 29 at 23:22
$begingroup$
thanks, makes sense
$endgroup$
– Dis-integrating
Jan 29 at 23:23
2
2
$begingroup$
You can have a sample space in which all outcomes are not equally likely. Who says you cannot?
$endgroup$
– David K
Jan 29 at 23:12
$begingroup$
You can have a sample space in which all outcomes are not equally likely. Who says you cannot?
$endgroup$
– David K
Jan 29 at 23:12
$begingroup$
then how do you define probability in any meaningful way?
$endgroup$
– Dis-integrating
Jan 29 at 23:22
$begingroup$
then how do you define probability in any meaningful way?
$endgroup$
– Dis-integrating
Jan 29 at 23:22
2
2
$begingroup$
A sample space is a set of outcomes. There is no requirement for those outcomes to be equally probable (and indeed that is why a probability space includes a probability function in its structure).
$endgroup$
– Graham Kemp
Jan 29 at 23:22
$begingroup$
A sample space is a set of outcomes. There is no requirement for those outcomes to be equally probable (and indeed that is why a probability space includes a probability function in its structure).
$endgroup$
– Graham Kemp
Jan 29 at 23:22
$begingroup$
thanks, makes sense
$endgroup$
– Dis-integrating
Jan 29 at 23:23
$begingroup$
thanks, makes sense
$endgroup$
– Dis-integrating
Jan 29 at 23:23
add a comment |
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2
$begingroup$
You can have a sample space in which all outcomes are not equally likely. Who says you cannot?
$endgroup$
– David K
Jan 29 at 23:12
$begingroup$
then how do you define probability in any meaningful way?
$endgroup$
– Dis-integrating
Jan 29 at 23:22
2
$begingroup$
A sample space is a set of outcomes. There is no requirement for those outcomes to be equally probable (and indeed that is why a probability space includes a probability function in its structure).
$endgroup$
– Graham Kemp
Jan 29 at 23:22
$begingroup$
thanks, makes sense
$endgroup$
– Dis-integrating
Jan 29 at 23:23