🚀 go-pugleaf

Jon Dodd wrote in message <360661F6.4DDCADE1@physiol.ox.ac.uk>...
....
>I have 1 normal distribution (in fact I have 2 identical normal
distributions
>but I posed the problem this way to make it simpler). I take random sample
A
>and then random sample B. if A>B then the value of A goes to group X. if
A<B
>then value A (value A again not B) goes to Y. Thus it is intuitive that X
>will have a greater mean than Y. They will differ from the original by the
>same amounts and be mirror images of each other about the mean.
>
>I have done some more thinking about this and the distributions of X and Y
>obviously must sum to the original distribution. If you draw this you get 2
>non normal distributions with differences from the mean of about 0.5 sd. My
>question again though is how do you go through a mathematical proof showing
>the exact values of the means and the common new sd? Is there an equation
>giving the shape of the new distributions? Is it just multiplying a
>cumulative gaussian (prob that A>B) by the original distribution - if so
how
>do you do this?
>


The distributions of X and Y are the distribution of the largest and the
smallest observation in a sample of 2 from a normal distribution
respectively. Properties of these distributions may be found under the
heading "order statistics" in statistical literature.

Jos Jansen.