Hi All, First of All, I am not a Statistics Expert by myself, however, I would like to raise another angle of this issue.
If instead of divide (or partition) into two separate normal distribution, I would do this into n separate normal distribution where n is the number of points constituting the original distribution N(50,5). What would happen then to the individual means and std ??? "gilgames" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > << > Folks, > > I have one question. Please let me know if any of you know the answer to > my question. > > I have a normal distribution with mean = 50 and standard deviation = 5 > I want to divide this distribution into two separate normal > distributions each with mean = 25 so that when I add them I will get my > original distribution. > > Do any one know how to find the two separate distributions? > > Is the answer distribution 1 : N(25,3) and distribution 2: N(25,4) correct ? > >> > > If you have two independent normal random set N(25,3) and N(25,4) and > add them together piecevise, you will get N(50, 5). In general for two > independent set the mean is the sum of the components and also the > variances are the sum of the variances of the components. > > If you reverse it and from a normal random set N(50,5) substract an > independent N(25,3) normal random set piecevise, then you will get N(25, > 5.831) being the new std = sqrt(std1**2 + std2**2) > > http://localhost/cgi-bin/igperl/igp.pl?dir=test&name=addeddistr > > > Now the insteresting point: If you have a normal random set N(50,5) and > make two distributions on that manner, that divide each number on the > ration of the expected new means ($a = $orig * $mean1 / $meanorig and > $b = $orig - $a) then the resulted standard deviation also will be > divided by the ration of the expected new means, on that manner that the > sum of the two standard deviations will be the original (if the given > new mean is larger than the orginal, then that std will be larger also), > so N(50,5) divided onto two equal half each element will result > N(50,2.5), N(50,2.5) sets > > http://localhost/cgi-bin/igperl/igp.pl?dir=test&name=dividedistr > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
