Probability without STD?

1. Dec 9, 2006

Poop-Loops

Is there a way to figure out the probability of getting a number if all you have is the mean? Everything I can find tells me I need the STD for that, but I don't have it given.

2. Dec 9, 2006

chroot

Staff Emeritus
Er, what? What does "getting a number" mean?

- Warren

3. Dec 9, 2006

Poop-Loops

Sorry. You have a mean number of an event occuring and then you want to find the probability of another event occuring (i.e. getting a number).

So for example you have that the mean is 5 and you want to find the probability of getting a 6.

And actually I'm fairly certain this is a Poisson distribution, so the STD is just the root of the mean. But, if you know of any way to find the probabilty using only the mean for a Gaussian distribution, please tell me, since I'm not 100% certain.

4. Dec 9, 2006

chroot

Staff Emeritus
Yeah, you need the entire probability distribution. If all you know is the mean, you know nothing about the distribution. Even the standard deviation is useless, unless you actually know a priori that the distribution is a normal distribution.

- Warren

5. Dec 9, 2006

Poop-Loops

I got it now.

You had the number of car accidents per a night, so what was the probability of getting a number the next night. Since you can't have less than 0, it HAD to be a Poisson distribution and not a normal one, right? Then I don't need the STD to calculate the probability.

6. Dec 9, 2006

chroot

Staff Emeritus
Sounds reasonable. I cannot say for sure that you're right, of course.

- Warren

7. Dec 9, 2006

Poop-Loops

Yeah, me neither, but it's the best thing I can think of.

8. Dec 9, 2006

Hurkyl

Staff Emeritus
Often, you would infer the distribution to use from what you're modelling. In particular, if you're modelling a Poisson process, then you'd use the Poisson distribution. If you aren't modelling a Poisson process, then you probably wouldn't use a Poisson distribution.

9. Dec 9, 2006

Poop-Loops

I know, I thought of that. I mean, Poisson stuff is used for things like radioactive decay, right? Not much to do with cars, which you would think would be a Gaussian distribution, but I can't find any formula for finding the probability of an event occuring if I don't have the STD, and also you can't have less than 0 events occuring, so you wouldn't be able to have the left tail of the distribution. We've only learned about two distributions in class, so I have to conclude that this is what I have to do. Or do you have any ideas?

EDIT: Actually, since we are given an interval (one night), and the accidents could occur at any time, it could follow a Poisson distribution... right?

Last edited: Dec 9, 2006
10. Dec 9, 2006

Hurkyl

Staff Emeritus
There's a definition of a Poisson process. Anything that is a Poisson process would be Poisson distributed. There's no reason to think different Poisson processes should have much to do with each other.

Why would you think that?

11. Dec 9, 2006

Poop-Loops

...ummm... because most things are... and I have nothing else to go by really hahaha

But no, I think it's best described as a Poisson distribution from what I read in my book, since it can't be less than 0 to even out the mean and it has to do with intervals.

12. Dec 9, 2006

Hurkyl

Staff Emeritus
Is that how your book defines "Poisson process"?

13. Dec 9, 2006

Poop-Loops

It doesn't. It only gives explains when Poisson distributions are used.

14. Dec 10, 2006

HallsofIvy

You are still talking very "sloppy". What could the "number of car accidents per night" possibly have to do with "getting a number the next night" (i.e. phone number of the girl you just met in a bar!).:rofl:

Oh, wait a minute! Possibly you mean "given the mean number of car accidents a night, find the probability that there will be a given number of car accidents the next night". That's not at all what you said!
You say "it HAD to be a Poisson distribution". And then say "I don't need the STD". Of course you do- you just assumed the STD: the Poisson distribution with the given mean. (One nice thing about the Poisson distribution is that it's standard deviation and other moments is the same as the mean- you are using a lot more information than you think!)