Date: Jul 1, 2009 9:03 PM
Author: Henry
Subject: Re: Somerhing´s not correct

www.applet-magic.com/samplemin.htm> it can be read:

******** If p(x) is the probability density function for a random variable x, let P(x) be the cumulative probability function; i.e.,
 P(x) = Intg(-infinity, x).p(z)dz

 The probability that the minimum of a sample of size n is x is given by
Prob.(min size n sample) = n[1- P(x)]^(n-1) * p(x)

 *********************************************

My comment

Suppose, for example,

 Uniform [0, 1] Distribution, P(x) = x, p(x) =1
 Prob.(min size n sample) = 21[1- x]^20 * 1
 If x=0.05 then results 7.528,
This is, no doubt, a remarkable thing (!!!). The Applet is so magic that it not available yet. Please, remove it! The writer did intend to say:
 ____Prob (min <=x) = 1- (1-F(x))^n

 ____1- (1-0.05)^21=0.659438______
For a continuous random variable, the probability that the minimum of a sample of size n is exactly x is given by 0. What the author probably intended to say was that the probability *density* of the minimum of a sample of size n is x is given by f(min size n sample) = n[1- P(x)]^(n-1) * p(x) There is nothing remarkable about a probability density being more than 1.
Note that the integral of f(x) dx with P(x) = x, p(x)=1 from x=0 to 0.05 is indeed about 0.659438...,
which hardly needs 8000000 runs round a simulation to calculate.

******************************

My response

__1__You agree, it´s evident, that the *genius* that posted such a thing should be severely adverted by the University.
__2__You are sufficiently smart to understand that the simulation is an addendum to the formula, or not?
__3__Your opinion what the author *intended to say* is a simple and unintelligent extrapolation. Doing so you think, in your *naivety*, people will to absolve him. Furthermore it was him (not me) that gave the formula of the probability of the minimum be x:  you should correct him as long as he published the post.
__4__Aspiring you to be known as a scrupulous person in Statistics, why you didn’t correct the error your fellow barbarous countryman got?. That was YOUR task.

Luis A. Afonso