Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.3 alpha 4/15/85; site pucc-h
Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!ihnp4!inuxc!pur-ee!pucc-j!pucc-h!ags
From: ags@pucc-h (Dave Seaman)
Newsgroups: net.puzzle
Subject: Re: random number wanted between neg inf and pos inf
Message-ID: <2533@pucc-h>
Date: Mon, 23-Dec-85 10:31:44 EST
Article-I.D.: pucc-h.2533
Posted: Mon Dec 23 10:31:44 1985
Date-Received: Wed, 25-Dec-85 01:18:23 EST
References: <33@decwrl.UUCP>
Reply-To: ags@pucc-h.UUCP (Dave Seaman)
Organization: Purdue University Computing Center
Lines: 22

A random variable is characterized by its distribution function.  If R
is the real number line, then a probability distribution is a function
F : R --> [0,1] with the properties

	(1) F is nondecreasing,

	(2) F is right-continuous (for our purposes we may as well
	    assume F is continuous),

	(3) F(x) --> 0 as x --> -infinity,

	(4) F(x) --> 1 as x --> +infinity.

F defines a probability measure on R such that F([a,b]) = F(b) - F(a).
For the distribution to be uniform on R, we have the added condition

	(5) F has constant slope on R.

Condition (5) is obviously incompatible with (3) and (4).  Therefore
there is no such thing as a uniform distribution on R.
-- 
Dave Seaman	  					pur-ee!pucc-h!ags