Hey,

Could I get a simple explanation for the equation below?

p(x)=limn0

n->oo n

Thanks.

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- Oct 20th 2007, 02:14 PMSeanCProbability question
Hey,

Could I get a simple explanation for the equation below?

p(x)=lim__n0__

n->oo n

Thanks. - Oct 20th 2007, 02:35 PMPlato
- Oct 20th 2007, 04:24 PMSeanC
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... - Oct 21st 2007, 01:24 AMCaptainBlack
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 - Oct 21st 2007, 05:53 AMSeanC