# Offbeat statistics, but fun! (1 Viewer)

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#### vtmemo

Okay, here's the deal.

We all know the law of independent probability after a broken sequence. For example, if you were to flip a coin 100 times, the first 90 times coming up heads and the last one tails. We all know that each flip is 'independent' of the last flip so long as they are taken as an individual occurence.

However, the odds of flipping a coin Heads 90 times in a row is relatively slim, thus making the odds of a Tails flip on the last one seem bigger. It's like saying "the odds against this streak occurring are high, so there is a higher probability that a flip will occur that breaks the run than one that continues it."

Here comes the big question: is quantum statistics self-defeating? That is, does observation on a quantum level change that which we observe because of sequential laws governing statistics?

For example, let's say there's an almost-infinitely improbable event that we wish to observe. Does the fact that we are observing every passing second of that event "not" occuring increase the probability of it actually occuring? I guess another way to say the idea would be:
"As the probability of something occurring approaches zero on a quantum level, the probability of it *actually* occurring under observation increases, in the sense that it will occur under observation AT ALL"

I dunno. Feels kinda like a Murphy's Law of event-related statistics, or some sort of "you can't observe it without changing it" theory.
I got bored at work

#### CRGreathouse

Homework Helper
It dounds like you're talking about moving from discrete -> discrete cases to continuous -> discrete (like the Poisson distribution). It's hard to compare the two!

#### Hurkyl

Staff Emeritus
Gold Member
It's like saying "the odds against this streak occurring are high, so there is a higher probability that a flip will occur that breaks the run than one that continues it."
This is wrong. The odds against 90 heads in a row aren't high if you've already seen 89...

Or to put it another way, out of 90 flips, getting 89 heads in a row followed by a tail is just as unlikely as getting 90 heads in a row.

We all know that each flip is 'independent' of the last flip so long as they are taken as an individual occurence.
Being independent means you can treat them each individually. If you couldn't do so, then they wouldn't be independent.

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#### EnumaElish

Homework Helper
The only sense in which I can relate to vtmemo's question is to think in terms of a hazard function. Every minute passing without a hazard occuring increases the chances that it will be observed in the next minute. There is a well-developed literature.

#### EnumaElish

Homework Helper
A (somewhat) related paradox is "barium (?) atoms will never reach the boiling point if they are being watched" (or "a watched pot never boils"). There was a thread on this somewhere on these forums. I think someone also published an article.

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