Finding Probability with Mean and Poisson Distribution

[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.

 

[chroot]

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

- Warren

 

[Poop-Loops]

Sorry. You have a mean number of an event occurring and then you want to find the probability of another event occurring (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.

 

[chroot]

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

 

[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.

 

[chroot]

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

- Warren

 

[Poop-Loops]

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

 

[Hurkyl]

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.

 

[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 occurring if I don't have the STD, and also you can't have less than 0 events occurring, 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?

 

[Hurkyl]

I know, I thought of that. I mean, Poisson stuff is used for things like radioactive decay, right? Not much to do with cars,

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.

which you would think would be a Gaussian distribution

Why would you think that?

 

[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.

 

[Hurkyl]

Is that how your book defines "Poisson process"?

 

[Poop-Loops]

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

 

[HallsofIvy]

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.

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!).

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!)