1. ## Probability question

Hey,

Could I get a simple explanation for the equation below?

p(x)=lim n0
n->oo n

Thanks.

2. Originally Posted by SeanC
Could I get a simple explanation for the equation below?
p(x)=lim n0
n->oo n
There is a very easy explication: as written it is mealingless.
What is the context of the question?
What are the definitions of the terms involved?

3. Originally Posted by Plato
There is a very easy explication: as written it is mealingless.
What is the context of the question?
What are the definitions of the terms involved?
Ah, sorry. If n trials of an experiment are run and produce n0 occurrences of x, the probably p of x is...(the equation).

I guess the only parts I don't quite understand are the LIM part and the n0 (why is there a 0...to distinguish it from "n"?).

I apologize if this sounds retarded, but it's been years since I even looked at an algebraic or calculus equation and I now have a need for it...

4. Originally Posted by SeanC
Hey,

Could I get a simple explanation for the equation below?

p(x)=lim n0
n->oo n

Thanks.
It is the standard frequentist definition of probability of outcome $\displaystyle x$. If you
repeat the experiment a large number $\displaystyle n$ of times, and record $\displaystyle n_0$ occurences
of out come $\displaystyle x$ we estimate the probability of $\displaystyle x$ as:

$\displaystyle \hat{p}(x) = \frac{n_0}{n}$

Then the definition of the probability of $\displaystyle x$ is the limit of such an estimator as $\displaystyle n \to \infty$.

This can be written as:

$\displaystyle p(x)=\lim_{n \to \infty} \frac{n_0}{n}$

but this is a abuse of notation from other parts of mathematics as this limit
is not the usual limit encountered in other parts of mathematics, and cannot
be evaluated.

(Just learn it, you will need it for your exam, but it is nonsense. There are
better defintions that you will encounter if you contine with the study of
probability)

RonL

5. Originally Posted by CaptainBlack
It is the standard frequentist definition of probability of outcome $\displaystyle x$. If you
repeat the experiment a large number $\displaystyle n$ of times, and record $\displaystyle n_0$ occurences
of out come $\displaystyle x$ we estimate the probability of $\displaystyle x$ as:

$\displaystyle \hat{p}(x) = \frac{n_0}{n}$

Then the definition of the probability of $\displaystyle x$ is the limit of such an estimator as $\displaystyle n \to \infty$.

This can be written as:

$\displaystyle p(x)=\lim_{n \to \infty} \frac{n_0}{n}$

but this is a abuse of notation from other parts of mathematics as this limit
is not the usual limit encountered in other parts of mathematics, and cannot
be evaluated.

(Just learn it, you will need it for your exam, but it is nonsense. There are
better defintions that you will encounter if you contine with the study of
probability)

RonL
Great, thank you.