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After doing an experiment as part of my university coursework and getting some funny results, one of the points I thought I would include in the write-up was the possibility of inadequate entropy added to one of the variables. I was hoping for a pointer with the math, however. Suppose you have a number of coins (call it x) that you are repeatedly throwing. The first toss is fair, but for each subsequent toss, there is a fixed probability of any coin retaining information about how it landed on the previous toss (for example, there is a p% chance for each coin on each toss that, rather than landing randomly, it will land on the reverse of the side it landed on in the previous toss). In the long run, what would be the expected proportions of tosses with i heads, for i = 0 to x? Cheers. -- 130.216.172.247 ( talk) 06:52, 18 April 2010 (UTC)
The answers above are largely irrelevant to the question. If you've specified that you've got probability p of landing on the side opposite the side you got last time, you've defined the problem. The question is not how big p is, given the physical conditions; the question is what is the probability distribution of the outcome give the value of p. It's a function of p. And obviously in this simple case knowing p is the same as knowing the correlation, but saying that doesn't answer the question.
You may want to think about equilibrium distributions of Markov chains. This is a fairly simple Markov chain. Michael Hardy ( talk) 00:57, 19 April 2010 (UTC)
How can I find the first number with more than N factors? 12.105.164.147 ( talk) 07:31, 18 April 2010 (UTC)
I've been trying to prove or disprove the following, but I'm not getting anywhere.
Suppose that for each cell in an unsolved soduku puzzle, you write out a list of possible values by looking at what other numbers are already used in that cell's row, column, and 3x3 block. This list is kept updated as the puzzle is being solved. Can the following statements be simultaneously true?
1. The soduku puzzle has one and only one solution. 2. All cells with only 1 possible value have already been assigned that value, and the list of possible values is updated afterwards. (In other words, every unfilled cell has 2 or more possible values.) 3. In each row, column, and 3x3 block, every number from 1 to 9 not already in that row, column, or block exists in the "possible" lists of 2 or more cells.
I think that #3 can't be true if #1 and #2 are because otherwise, there would be multiple solutions to the puzzle. I can't prove this, however. -- 99.237.234.104 ( talk) 17:31, 18 April 2010 (UTC)
Suppose we have an earthlike planet, called Urf, which needs to be populated. Every year, 500,000 settlers arrive (250,000 female and 250,000 male). These settlers are evenly distributed between the ages of 20 and 40. They're very healthy, so for simplicity's sake, let's assume that they (and their descendants) all live to be 100 years old. We've recruited people who want large families, so the fertility rate is 4.0 births per woman. Again for simplicity's sake, let's assume that our female settlers exhibit a constant rate of fertility between the ages of 20 and 40, and no fertility before and after. Given these values, what will be Urf's population in 10, 50 and 100 years? -- Lazar Taxon ( talk) 21:05, 18 April 2010 (UTC)
Year | Population |
---|---|
0 | 500000 |
10 | 3750000 |
20 | 9500000 |
30 | 17500000 |
40 | 26000000 |
50 | 37500000 |
60 | 53750000 |
70 | 72500000 |
80 | 94500000 |
90 | 122000000 |
100 | 157000000 |
110 | 197750000 |
120 | 247250000 |
130 | 309750000 |
140 | 385500000 |
150 | 475750000 |
"Constant rate of fertility" between the ages of 20 and 40, and having exactly four babies, sounds as if maybe it could mean each woman first gives birth when she's 1/5 of the way from 20 to 40, i.e. she's 24, then again at 2/5, then 3/5, then 4/5, so the ages are 24, 28, 32, 36. Or maybe it could mean the first baby is born when she's 20, then 26 + 2/3, then 33 + 1/3, then 40. Michael Hardy ( talk) 00:51, 19 April 2010 (UTC)
Except that all these simplifying assumptions seem out of place if you're bringing in stochasticity. Michael Hardy ( talk) 03:07, 21 April 2010 (UTC)
Mathematics desk | ||
---|---|---|
< April 17 | << Mar | April | May >> | April 19 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
After doing an experiment as part of my university coursework and getting some funny results, one of the points I thought I would include in the write-up was the possibility of inadequate entropy added to one of the variables. I was hoping for a pointer with the math, however. Suppose you have a number of coins (call it x) that you are repeatedly throwing. The first toss is fair, but for each subsequent toss, there is a fixed probability of any coin retaining information about how it landed on the previous toss (for example, there is a p% chance for each coin on each toss that, rather than landing randomly, it will land on the reverse of the side it landed on in the previous toss). In the long run, what would be the expected proportions of tosses with i heads, for i = 0 to x? Cheers. -- 130.216.172.247 ( talk) 06:52, 18 April 2010 (UTC)
The answers above are largely irrelevant to the question. If you've specified that you've got probability p of landing on the side opposite the side you got last time, you've defined the problem. The question is not how big p is, given the physical conditions; the question is what is the probability distribution of the outcome give the value of p. It's a function of p. And obviously in this simple case knowing p is the same as knowing the correlation, but saying that doesn't answer the question.
You may want to think about equilibrium distributions of Markov chains. This is a fairly simple Markov chain. Michael Hardy ( talk) 00:57, 19 April 2010 (UTC)
How can I find the first number with more than N factors? 12.105.164.147 ( talk) 07:31, 18 April 2010 (UTC)
I've been trying to prove or disprove the following, but I'm not getting anywhere.
Suppose that for each cell in an unsolved soduku puzzle, you write out a list of possible values by looking at what other numbers are already used in that cell's row, column, and 3x3 block. This list is kept updated as the puzzle is being solved. Can the following statements be simultaneously true?
1. The soduku puzzle has one and only one solution. 2. All cells with only 1 possible value have already been assigned that value, and the list of possible values is updated afterwards. (In other words, every unfilled cell has 2 or more possible values.) 3. In each row, column, and 3x3 block, every number from 1 to 9 not already in that row, column, or block exists in the "possible" lists of 2 or more cells.
I think that #3 can't be true if #1 and #2 are because otherwise, there would be multiple solutions to the puzzle. I can't prove this, however. -- 99.237.234.104 ( talk) 17:31, 18 April 2010 (UTC)
Suppose we have an earthlike planet, called Urf, which needs to be populated. Every year, 500,000 settlers arrive (250,000 female and 250,000 male). These settlers are evenly distributed between the ages of 20 and 40. They're very healthy, so for simplicity's sake, let's assume that they (and their descendants) all live to be 100 years old. We've recruited people who want large families, so the fertility rate is 4.0 births per woman. Again for simplicity's sake, let's assume that our female settlers exhibit a constant rate of fertility between the ages of 20 and 40, and no fertility before and after. Given these values, what will be Urf's population in 10, 50 and 100 years? -- Lazar Taxon ( talk) 21:05, 18 April 2010 (UTC)
Year | Population |
---|---|
0 | 500000 |
10 | 3750000 |
20 | 9500000 |
30 | 17500000 |
40 | 26000000 |
50 | 37500000 |
60 | 53750000 |
70 | 72500000 |
80 | 94500000 |
90 | 122000000 |
100 | 157000000 |
110 | 197750000 |
120 | 247250000 |
130 | 309750000 |
140 | 385500000 |
150 | 475750000 |
"Constant rate of fertility" between the ages of 20 and 40, and having exactly four babies, sounds as if maybe it could mean each woman first gives birth when she's 1/5 of the way from 20 to 40, i.e. she's 24, then again at 2/5, then 3/5, then 4/5, so the ages are 24, 28, 32, 36. Or maybe it could mean the first baby is born when she's 20, then 26 + 2/3, then 33 + 1/3, then 40. Michael Hardy ( talk) 00:51, 19 April 2010 (UTC)
Except that all these simplifying assumptions seem out of place if you're bringing in stochasticity. Michael Hardy ( talk) 03:07, 21 April 2010 (UTC)