"Chia C Chong" <[EMAIL PROTECTED]> wrote in message
news:<a5g27d$e57$[EMAIL PROTECTED]>...
> Hi!
>
> I have a set of random numbers and if I know their expectation/mean, would
> it be possible to deduce a PDF to describe the distribution of them?
Knowing the mean tells you (almost) nothing about the form of the PDF.
However, if you are considering a particular family of PDFs (for
whatever reason), it should usually be possible to specify the mean
(in some cases fixing a parameter, in other cases introducing an
equation relating the parameters, so that you can reduce the dimension
of the parameter vector by 1).
> How do
> I make sure that when I generating these random numbers using the PDF I
> obtained, it will give me th correct mean/expectation value?
It depends on what you mean here - you must be careful to distinguish
between the population mean (which you say is known) and the sample
mean.
If you mean make it so you are generating from a distribution which
has the correct population mean, that's taken care of above.
If you mean generate so the sample mean is equal to the population
mean, why would you want to do that?
Consider the mean from n rolls of a (hypothetical) fair six-sided die
numbered 1 to 6. If it really is fair, I *know* the population mean is
3.5. Yet the sample mean is almost never 3.5, even though I know the
population mean exactly. If I wanted to simulate rolls from this die,
I would not try to make the sample mean 3.5.
Think on this: Let's assume I want a sample of size 1. To make it have
the known mean I have to set it equal to the known mean. Does it come
from the right distribution? Not at all! It comes from a distribution
with all the probability at the known mean. Now I want to enlarge the
sample by adding a second observation. What value will that have? As I
keep adding to my sample, I have to keep generating the same value
over and over.
(There may be some reason you want to generate in such a way that the
sample mean is constant, but I doubt it - and you won't be able to
have independent observations if you do.)
Glen
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