"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 ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =================================================================