Horst Kraemer <[EMAIL PROTECTED]> writes: > On Mon, 11 Aug 2003 17:10:38 -0500, "K L" <[EMAIL PROTECTED]> wrote: > > > 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 X is N(25,3) and Y is N(25,3) and X and Y are *uncorreleted* RVs,
I think you mean *independent*. Let U be N(25,3) and V be +1 or -1 with pr 1/2 each Set X = U Y = U*V Now X and Y are _uncorrelated_, each has a N(25,3) when considered on their own. Note, (X,Y) is not jointly Gaussian, but this was not claimed above. However, Z = X+Y is *not* Gaussian. Half the time, when V is -1, Z = 0. The other half the time, when V is +1, it is normal but twice as large. > then Z=X+Y is N(50,5). If you mean by "add two distributions" that you > are going to add the RVs defined by these distributions then your > answer is correct - if you add the condition that X and Y are > uncorrelated. > > -- > Horst > -- Johan KULLSTAM <[EMAIL PROTECTED]> sysengr . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
