You are given a machine made by scientists that they say is perfectly random. All the machine does is display ten numbers every year on the same day. But the machine has just been made. So on its very first display of numbers, it lists out ten 5's. Do we assume it's random or assume the scientists made a mistake, in which case the machine is deterministic? — Gregory
What is the prior probability that you are you, and sitting in this particular room with its particular arrangement of stuff? What are the odds that there's any stuff at all? The odds are virtually zero. Yet here you are. — fishfry
Also, if 100 events have an equal probability of happening they are said to be random but one of them does happen and there must be a reason for that. — EnPassant
Lottery paradox. It's rational to conclude that you won't win, therefore you shouldn't play. But somebody must win.
That's why they say god throws dice. Nobody can generate random numbers, not because it's impossible, but because it is not possible to test for it being truly random. — god must be atheist
Back in my meteorology days one approach was to measure small changes in atmospheric pressure. But not a guarantee of randomness. — jgill
Btw, do you buy the idea that a sequence is random if the next cannot be guessed from the series - which probably requires actually generating the next number? . — tim wood
And they never tell you that any number you choose is correct. Of course the idea is that "they" have a rule in mind that you're supposed to divine. But if you choose your own rule, then your good!I've been stumped by brain teasers that have you try to determine the next number in a sequence, — jgill
The possibility space includes the number 5555555555 and it being the first number displayed doesn't, in any way, aid us in deciding whether the machine is a true random number generator or not. — TheMadFool
The more spread-out strings are more common and therefore more likely. The string is all 5s has only 9 other strings of similar extremity. That's a 1 in 10^9 chance of such a concentration, which is strong evidence against randomness. — T H E
While each string of digits is equally likely, we can categorize strings by how spread out over the 10 categories they are. The more spread-out strings are more common and therefore more likely. The string is all 5s has only 9 other strings of similar extremity. That's a 1 in 10^9 chance of such a concentration, which is strong evidence against randomness. — T H E
https://en.wikipedia.org/wiki/P-valueIn null hypothesis significance testing, the p-value[note 1] is the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct.[2][3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Reporting p-values of statistical tests is common practice in academic publications of many quantitative fields. Since the precise meaning of p-value is hard to grasp, misuse is widespread and has been a major topic in metascience.[4][5]
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Null hypothesis testing is a reductio ad absurdum argument adapted to statistics. In essence, a claim is assumed valid if its counterclaim is highly implausible.
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Thus, the only hypothesis that needs to be specified in this test and which embodies the counterclaim is referred to as the null hypothesis; that is, the hypothesis to be nullified. A result is said to be statistically significant if it allows us to reject the null hypothesis. The result, being statistically significant, was highly improbable if the null hypothesis is assumed to be true. A rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis. — wiki
That's only because you're lumping all the "evenly spread" events together. There are far more of them. Whatever outcome you got was incredibly unlikely. The fact that it's a member of an arbitrarily large class of outcomes doesn't make any difference except psychologically. — fishfry
But what then do you make of testing the coin for fairness as in my reply to tim? — T H E
We can generate completely deterministic sequences of numbers that satisfy every known statistical test for randomness. — fishfry
we seem to have some intuition of perfect randomness — T H E
There seems to me something infinite about randomness. — Gregory
A test would be whether the next numbers in the series could be predicted - if the series proved to be an oracle for its own successive members. — tim wood
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