Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

(e.g. X), their realizations by observation with lower case letters
(e.g. x), and their true values with the subscript "On (e.g. x0).
Let f(X) be the pdf of a variab1.e X. Then the probabi.lity that a
realisation x exceeds a value G is
m
a = J f(X)dX.
G
Hence, there is a "confidence" of
f3 = (1-a) . 100% that x does not
exceed G.
The following pdf's will be needed in this section:
k" C;
(1) The "Gaussian Normal Distribution" of a normalized variable
with the dispersion 1 and zero mean value:
(2) The X2-distribution for v degrees of freedom:
, (3) The Fisher-distribution for N and V2 degrees of freedom:
1
'These distributions are encountered in the fol.lowing problems:
Consider a random variable X which is normally distributed with
Let - 1 n
X = -
n C Xi
i=l
be the, realized .sample mean value of n realizations of X. These
mean val.ues .are also normally distributed with the dispersj.on
accordj-ng to the "central 1.imi-t theorem".