Probability of placing colored balls into multiple colored urns [on hold]
-1
I have a large urn containing n balls, each of which is one of m different colors. What is the probability of selecting k balls at random with r unique colors?
My interest is in n=10^7, m=10^6, k~25, and 1 <= r <= k.
combinatorics
asked Jan 4 at 13:52
Ed GiorgioEd Giorgio
1
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put on hold as off-topic by amWhy, jgon, Shailesh, Leucippus, José Carlos Santos Jan 5 at 11:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, jgon, Shailesh, Leucippus, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
-1
I have a large urn containing n balls, each of which is one of m different colors. What is the probability of selecting k balls at random with r unique colors?
My interest is in n=10^7, m=10^6, k~25, and 1 <= r <= k.
combinatorics
asked Jan 4 at 13:52
Ed GiorgioEd Giorgio
1
New contributor
Ed Giorgio is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by amWhy, jgon, Shailesh, Leucippus, José Carlos Santos Jan 5 at 11:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, jgon, Shailesh, Leucippus, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
Are the colours distributed randomly, so there is a (theoretical) chance that there are colours missing entirely? Also, note that with $m, n$ that large and $k$ that small, you can surely get five or six significant digits correct pretending that the balls are just generated as you draw them and not taken from a finite supply.
– Arthur
Jan 4 at 13:53
The colors are all observed at least once. They are not uniformly distributed. The distribution has a fat tail and is best modeled using a power-law distribution.
– Ed Giorgio
Jan 4 at 14:01
yes, you can assume that the balls are generated as you draw them and not taken from a finite supply
– Ed Giorgio
Jan 4 at 14:15
And you say the colours aren't uniformly distributed. That means that some colours are more common. How much more common?
– Arthur
Jan 4 at 14:21
Yes, some colors are more common. They obey a power-law distribution. This means that Pr[x] = a*x^(-alpha). alpha is known as the scaling parameter. This distribution is very common in many areas of science. An example is large graphs from social networking, where people connect to a small number of people frequently, and a large number of people infrequently.
– Ed Giorgio
Jan 4 at 16:52
add a comment |
-1
-1
-1
I have a large urn containing n balls, each of which is one of m different colors. What is the probability of selecting k balls at random with r unique colors?
My interest is in n=10^7, m=10^6, k~25, and 1 <= r <= k.
combinatorics
asked Jan 4 at 13:52
Ed GiorgioEd Giorgio
1
New contributor
Ed Giorgio is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have a large urn containing n balls, each of which is one of m different colors. What is the probability of selecting k balls at random with r unique colors?
My interest is in n=10^7, m=10^6, k~25, and 1 <= r <= k.
combinatorics
combinatorics
asked Jan 4 at 13:52
Ed GiorgioEd Giorgio
1
New contributor
Ed Giorgio is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 13:52
Ed GiorgioEd Giorgio
1
New contributor
Ed Giorgio is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 13:52
Ed GiorgioEd Giorgio
1
New contributor
Ed Giorgio is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 13:52
Ed GiorgioEd Giorgio
1
asked Jan 4 at 13:52
Ed GiorgioEd Giorgio
1
1
New contributor
Ed Giorgio is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ed Giorgio is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ed Giorgio is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by amWhy, jgon, Shailesh, Leucippus, José Carlos Santos Jan 5 at 11:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, jgon, Shailesh, Leucippus, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by amWhy, jgon, Shailesh, Leucippus, José Carlos Santos Jan 5 at 11:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, jgon, Shailesh, Leucippus, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
Are the colours distributed randomly, so there is a (theoretical) chance that there are colours missing entirely? Also, note that with $m, n$ that large and $k$ that small, you can surely get five or six significant digits correct pretending that the balls are just generated as you draw them and not taken from a finite supply.
– Arthur
Jan 4 at 13:53
The colors are all observed at least once. They are not uniformly distributed. The distribution has a fat tail and is best modeled using a power-law distribution.
– Ed Giorgio
Jan 4 at 14:01
yes, you can assume that the balls are generated as you draw them and not taken from a finite supply
– Ed Giorgio
Jan 4 at 14:15
And you say the colours aren't uniformly distributed. That means that some colours are more common. How much more common?
– Arthur
Jan 4 at 14:21
Yes, some colors are more common. They obey a power-law distribution. This means that Pr[x] = a*x^(-alpha). alpha is known as the scaling parameter. This distribution is very common in many areas of science. An example is large graphs from social networking, where people connect to a small number of people frequently, and a large number of people infrequently.
– Ed Giorgio
Jan 4 at 16:52
add a comment |
Are the colours distributed randomly, so there is a (theoretical) chance that there are colours missing entirely? Also, note that with $m, n$ that large and $k$ that small, you can surely get five or six significant digits correct pretending that the balls are just generated as you draw them and not taken from a finite supply.
– Arthur
Jan 4 at 13:53
The colors are all observed at least once. They are not uniformly distributed. The distribution has a fat tail and is best modeled using a power-law distribution.
– Ed Giorgio
Jan 4 at 14:01
yes, you can assume that the balls are generated as you draw them and not taken from a finite supply
– Ed Giorgio
Jan 4 at 14:15
And you say the colours aren't uniformly distributed. That means that some colours are more common. How much more common?
– Arthur
Jan 4 at 14:21
Yes, some colors are more common. They obey a power-law distribution. This means that Pr[x] = a*x^(-alpha). alpha is known as the scaling parameter. This distribution is very common in many areas of science. An example is large graphs from social networking, where people connect to a small number of people frequently, and a large number of people infrequently.
– Ed Giorgio
Jan 4 at 16:52
Are the colours distributed randomly, so there is a (theoretical) chance that there are colours missing entirely? Also, note that with $m, n$ that large and $k$ that small, you can surely get five or six significant digits correct pretending that the balls are just generated as you draw them and not taken from a finite supply.
– Arthur
Jan 4 at 13:53
Are the colours distributed randomly, so there is a (theoretical) chance that there are colours missing entirely? Also, note that with $m, n$ that large and $k$ that small, you can surely get five or six significant digits correct pretending that the balls are just generated as you draw them and not taken from a finite supply.
– Arthur
Jan 4 at 13:53
The colors are all observed at least once. They are not uniformly distributed. The distribution has a fat tail and is best modeled using a power-law distribution.
– Ed Giorgio
Jan 4 at 14:01
The colors are all observed at least once. They are not uniformly distributed. The distribution has a fat tail and is best modeled using a power-law distribution.
– Ed Giorgio
Jan 4 at 14:01
yes, you can assume that the balls are generated as you draw them and not taken from a finite supply
– Ed Giorgio
Jan 4 at 14:15
yes, you can assume that the balls are generated as you draw them and not taken from a finite supply
– Ed Giorgio
Jan 4 at 14:15
And you say the colours aren't uniformly distributed. That means that some colours are more common. How much more common?
– Arthur
Jan 4 at 14:21
And you say the colours aren't uniformly distributed. That means that some colours are more common. How much more common?
– Arthur
Jan 4 at 14:21
Yes, some colors are more common. They obey a power-law distribution. This means that Pr[x] = a*x^(-alpha). alpha is known as the scaling parameter. This distribution is very common in many areas of science. An example is large graphs from social networking, where people connect to a small number of people frequently, and a large number of people infrequently.
– Ed Giorgio
Jan 4 at 16:52
Yes, some colors are more common. They obey a power-law distribution. This means that Pr[x] = a*x^(-alpha). alpha is known as the scaling parameter. This distribution is very common in many areas of science. An example is large graphs from social networking, where people connect to a small number of people frequently, and a large number of people infrequently.
– Ed Giorgio
Jan 4 at 16:52
add a comment |
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Are the colours distributed randomly, so there is a (theoretical) chance that there are colours missing entirely? Also, note that with $m, n$ that large and $k$ that small, you can surely get five or six significant digits correct pretending that the balls are just generated as you draw them and not taken from a finite supply.
– Arthur
Jan 4 at 13:53
The colors are all observed at least once. They are not uniformly distributed. The distribution has a fat tail and is best modeled using a power-law distribution.
– Ed Giorgio
Jan 4 at 14:01
yes, you can assume that the balls are generated as you draw them and not taken from a finite supply
– Ed Giorgio
Jan 4 at 14:15
And you say the colours aren't uniformly distributed. That means that some colours are more common. How much more common?
– Arthur
Jan 4 at 14:21
Yes, some colors are more common. They obey a power-law distribution. This means that Pr[x] = a*x^(-alpha). alpha is known as the scaling parameter. This distribution is very common in many areas of science. An example is large graphs from social networking, where people connect to a small number of people frequently, and a large number of people infrequently.
– Ed Giorgio
Jan 4 at 16:52