If $S=1,2,3$ and $P(1,2) = 1/3$ and $P(2,3)=2/3$, what is $P(1),P(2),P(3)$
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If $S=1,2,3$ and $P(1,2) = 1/3$ and $P(2,3)=2/3$ , what is $P(1),P(2),P(3)$?
This can be shown in a linear system as follows (ignoring the inner set notation):
$$P(1) + P(2) + P(3) = 1$$
$$P(1)+P(2) = 1/3$$
$$P(2) + P(3) = 2/3$$
Solving the system gives us that $P(3)=2/3, P(2) =0, P(1) = 1/3$
But $P(2) = 0$ would not make it part of the sample space since it is not an outcome. Where have I gone wrong here?
probability statistics
asked Sep 6 at 2:06
K Split X
3,929929
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up vote
0
down vote
favorite
If $S=1,2,3$ and $P(1,2) = 1/3$ and $P(2,3)=2/3$ , what is $P(1),P(2),P(3)$?
This can be shown in a linear system as follows (ignoring the inner set notation):
$$P(1) + P(2) + P(3) = 1$$
$$P(1)+P(2) = 1/3$$
$$P(2) + P(3) = 2/3$$
Solving the system gives us that $P(3)=2/3, P(2) =0, P(1) = 1/3$
But $P(2) = 0$ would not make it part of the sample space since it is not an outcome. Where have I gone wrong here?
probability statistics
asked Sep 6 at 2:06
K Split X
3,929929
An outcome with probability zero is still part of the sample space, why do you think it isn't? That's where you went wrong. (Meaning, you were 99.9% right, and stumbled over a non-issue right at the end.)
– mathguy
Sep 6 at 2:15
Well If you had a 6 sided die would you consider the outcome $7$ in the sample space?
– K Split X
Sep 6 at 2:18
No. But you are considering things in the wrong order. First you need to specify the sample space, then the $sigma$-algebra of events on which you define probability, and then the probability measure. (For finite sample spaces, first you specify the sample space, and only then the probability function.) There is no requirement that the only event with probability 0 be the empty event.
– mathguy
Sep 6 at 2:22
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If $S=1,2,3$ and $P(1,2) = 1/3$ and $P(2,3)=2/3$ , what is $P(1),P(2),P(3)$?
This can be shown in a linear system as follows (ignoring the inner set notation):
$$P(1) + P(2) + P(3) = 1$$
$$P(1)+P(2) = 1/3$$
$$P(2) + P(3) = 2/3$$
Solving the system gives us that $P(3)=2/3, P(2) =0, P(1) = 1/3$
But $P(2) = 0$ would not make it part of the sample space since it is not an outcome. Where have I gone wrong here?
probability statistics
asked Sep 6 at 2:06
K Split X
3,929929
If $S=1,2,3$ and $P(1,2) = 1/3$ and $P(2,3)=2/3$ , what is $P(1),P(2),P(3)$?
This can be shown in a linear system as follows (ignoring the inner set notation):
$$P(1) + P(2) + P(3) = 1$$
$$P(1)+P(2) = 1/3$$
$$P(2) + P(3) = 2/3$$
Solving the system gives us that $P(3)=2/3, P(2) =0, P(1) = 1/3$
But $P(2) = 0$ would not make it part of the sample space since it is not an outcome. Where have I gone wrong here?
probability statistics
probability statistics
asked Sep 6 at 2:06
K Split X
3,929929
asked Sep 6 at 2:06
K Split X
3,929929
asked Sep 6 at 2:06
K Split X
3,929929
asked Sep 6 at 2:06
K Split X
3,929929
asked Sep 6 at 2:06
K Split X
3,929929
3,929929
An outcome with probability zero is still part of the sample space, why do you think it isn't? That's where you went wrong. (Meaning, you were 99.9% right, and stumbled over a non-issue right at the end.)
– mathguy
Sep 6 at 2:15
Well If you had a 6 sided die would you consider the outcome $7$ in the sample space?
– K Split X
Sep 6 at 2:18
No. But you are considering things in the wrong order. First you need to specify the sample space, then the $sigma$-algebra of events on which you define probability, and then the probability measure. (For finite sample spaces, first you specify the sample space, and only then the probability function.) There is no requirement that the only event with probability 0 be the empty event.
– mathguy
Sep 6 at 2:22
add a comment |Â
An outcome with probability zero is still part of the sample space, why do you think it isn't? That's where you went wrong. (Meaning, you were 99.9% right, and stumbled over a non-issue right at the end.)
– mathguy
Sep 6 at 2:15
Well If you had a 6 sided die would you consider the outcome $7$ in the sample space?
– K Split X
Sep 6 at 2:18
No. But you are considering things in the wrong order. First you need to specify the sample space, then the $sigma$-algebra of events on which you define probability, and then the probability measure. (For finite sample spaces, first you specify the sample space, and only then the probability function.) There is no requirement that the only event with probability 0 be the empty event.
– mathguy
Sep 6 at 2:22
An outcome with probability zero is still part of the sample space, why do you think it isn't? That's where you went wrong. (Meaning, you were 99.9% right, and stumbled over a non-issue right at the end.)
– mathguy
Sep 6 at 2:15
An outcome with probability zero is still part of the sample space, why do you think it isn't? That's where you went wrong. (Meaning, you were 99.9% right, and stumbled over a non-issue right at the end.)
– mathguy
Sep 6 at 2:15
Well If you had a 6 sided die would you consider the outcome $7$ in the sample space?
– K Split X
Sep 6 at 2:18
Well If you had a 6 sided die would you consider the outcome $7$ in the sample space?
– K Split X
Sep 6 at 2:18
No. But you are considering things in the wrong order. First you need to specify the sample space, then the $sigma$-algebra of events on which you define probability, and then the probability measure. (For finite sample spaces, first you specify the sample space, and only then the probability function.) There is no requirement that the only event with probability 0 be the empty event.
– mathguy
Sep 6 at 2:22
No. But you are considering things in the wrong order. First you need to specify the sample space, then the $sigma$-algebra of events on which you define probability, and then the probability measure. (For finite sample spaces, first you specify the sample space, and only then the probability function.) There is no requirement that the only event with probability 0 be the empty event.
– mathguy
Sep 6 at 2:22
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
We call an outcome impossible when it is not an element in the sample space. Â Impossible outcomes are considered to have a probability of zero.
However elements that are in the sample space may still have a probability measure of zero. Â These are possible outcomes that are just considered too improbable to give a positive measure.
Having $mathsf P(2)=0$ when $2$ is an element of the sample space is not a problem.
And you have not gone wrong. That is the answer.
answered Sep 6 at 3:53
Graham Kemp
81.4k43275
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
We call an outcome impossible when it is not an element in the sample space. Â Impossible outcomes are considered to have a probability of zero.
However elements that are in the sample space may still have a probability measure of zero. Â These are possible outcomes that are just considered too improbable to give a positive measure.
Having $mathsf P(2)=0$ when $2$ is an element of the sample space is not a problem.
And you have not gone wrong. That is the answer.
answered Sep 6 at 3:53
Graham Kemp
81.4k43275
add a comment |Â
up vote
0
down vote
accepted
We call an outcome impossible when it is not an element in the sample space. Â Impossible outcomes are considered to have a probability of zero.
However elements that are in the sample space may still have a probability measure of zero. Â These are possible outcomes that are just considered too improbable to give a positive measure.
Having $mathsf P(2)=0$ when $2$ is an element of the sample space is not a problem.
And you have not gone wrong. That is the answer.
answered Sep 6 at 3:53
Graham Kemp
81.4k43275
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
We call an outcome impossible when it is not an element in the sample space. Â Impossible outcomes are considered to have a probability of zero.
However elements that are in the sample space may still have a probability measure of zero. Â These are possible outcomes that are just considered too improbable to give a positive measure.
Having $mathsf P(2)=0$ when $2$ is an element of the sample space is not a problem.
And you have not gone wrong. That is the answer.
answered Sep 6 at 3:53
Graham Kemp
81.4k43275
We call an outcome impossible when it is not an element in the sample space. Â Impossible outcomes are considered to have a probability of zero.
However elements that are in the sample space may still have a probability measure of zero. Â These are possible outcomes that are just considered too improbable to give a positive measure.
Having $mathsf P(2)=0$ when $2$ is an element of the sample space is not a problem.
And you have not gone wrong. That is the answer.
answered Sep 6 at 3:53
Graham Kemp
81.4k43275
answered Sep 6 at 3:53
Graham Kemp
81.4k43275
answered Sep 6 at 3:53
Graham Kemp
81.4k43275
answered Sep 6 at 3:53
Graham Kemp
81.4k43275
81.4k43275
add a comment |Â
add a comment |Â
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An outcome with probability zero is still part of the sample space, why do you think it isn't? That's where you went wrong. (Meaning, you were 99.9% right, and stumbled over a non-issue right at the end.)
– mathguy
Sep 6 at 2:15
Well If you had a 6 sided die would you consider the outcome $7$ in the sample space?
– K Split X
Sep 6 at 2:18
No. But you are considering things in the wrong order. First you need to specify the sample space, then the $sigma$-algebra of events on which you define probability, and then the probability measure. (For finite sample spaces, first you specify the sample space, and only then the probability function.) There is no requirement that the only event with probability 0 be the empty event.
– mathguy
Sep 6 at 2:22