21–30 of 38 posts
One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…
One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…
I do wonder if that is down to sample size. For example, I wrote a program to simulate the roll of a dice. There is a one in 6 chance of getting any one number. But roll it 6 million times, you'll be very close to have each number 1 million times. So I would anticipate the clumping to even out as the sample size increases. Or maybe the evening out is a large collection of clumps. Anyone know if this is the correct wa…
Are you saying we need to crash more planes? That seems a little harsh just to get crashes coming at a consistent rate. ;-)
One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…
Perhaps just an artifact of a weak PRNG or not truly uniform distribution?
One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…
The iPod shuffle algo was an example of this. It just didn't feel "random" enough for people to have a truly random generator.
Earlier quoted context omitted.
Well depends of what you mean by very close. It's the relative numbers that approaches the true distribution, not the absolute numbers. Do the experiment you decribe and look at the numbers.
This is what I mean: var results = [0,0,0,0,0,0]; for (var i = 0; i The results are: [1002140, 999355, 1000009, 1000401, 1000014, 998081] Basically, they are all within 1% tolerance of each number getting 1 million occurrences. So when you look at the clumping on random dots on a screen, given a large enough sample size, I would anticipate that the probability of keeping a clumped visual distribution would become qui…
The problem is when you get less samples than slots. For example if you roll 3 dices, you should get "1/2" hits for each result. So the question is: How probable is that one result is repeated? (i.e. you get two equal dices out of the three)
[spoiler alert]
All equal: 3%
Two equal and one different: 42%
Three different: 55%
"Intuitively", it's expected that with a uniform distribution you get something like 1% + 9% + 90% instead (this numbers are completely made up). Most people don't expect that the probability of getting a repeated dice is so close to the probability of getting all of them different.
"If there is a crash on 1 August, the chance that the next crash occurs one day later on 2 August is 1/365. But the chance the next crash is on 3 August is (364/365) x (1/365), because the next crash occurs on 3 August only if there is no crash on 2 August." Is this not the gambler's fallacy? Shouldn't the odds be unaffected by a previous crash?
In this case I would agree with you. I don't understand the reasoning for the last sentence at all.
The gambler fallacy would be "I have seen 9 days without crash, on the 10th day there is higher odds of crash". But you are not asking this, you are asking: "What is the chance that in the next 10 days, exactly first 9 days would be no-crash and on the 10th day there is a crash".
EDIT: Also, another view:
If you have seen 9 blacks in a row, there is an even chance 1/2 (roulette without zero) that the next will be black or red. Because in all sequences of length 10 starting with 9 blacks (this is given, you observed this), there is equal number of those with 9 consecutive blacks and a red and of those with 9 consecutive blacks and a black. This is gambler fallacy, believing that after repeated colour, you have higher chance of the other colour.
Here, you are asking: how many of all sequences of length 10 have exactly 9 blacks and 1 red. And there are all kinds of sequences with 1 red in first 9 places, 2 reds, 3 reds, etc., so the odds of observing the 9 blacks in a row in the first place before asking about the 10th spin is lower, but it does not change the odds of the 10th spin itself.
Earlier quoted context omitted.
Perhaps just an artifact of a weak PRNG or not truly uniform distribution?
No. A truly uniform random distribution indeed has "clumps".
Edit: I wrote a program[1] to fill random pixels based on rand/modulo and mersenne twister/uniform distribution and I could not tell the difference in the generates images.
One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…
I do wonder if that is down to sample size. For example, I wrote a program to simulate the roll of a dice. There is a one in 6 chance of getting any one number. But roll it 6 million times, you'll be very close to have each number 1 million times. So I would anticipate the clumping to even out as the sample size increases. Or maybe the evening out is a large collection of clumps. Anyone know if this is the correct wa…
It would probably true for that too but as another comment says, we don't want to have an increased sample size here!
One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…
I do wonder if that is down to sample size. For example, I wrote a program to simulate the roll of a dice. There is a one in 6 chance of getting any one number. But roll it 6 million times, you'll be very close to have each number 1 million times. So I would anticipate the clumping to even out as the sample size increases. Or maybe the evening out is a large collection of clumps. Anyone know if this is the correct wa…
Pleases mark as 2014 ... I also believe this is a repeat but can't seem to find the original.
I had tried the Algolia search box from my tablet and got no results. Using Google (constrained to HN) brought up today's discussion and the one from last year.
site:news.ycombinator.com plane crash cluster