48
Chapter 2
with
~2~ _ ~(6x’) 2 and ~y2 _
the approximate
standard deviation for a function is
I
-
2
"n 1/2
(2.16)
where ~xj is standard deviation of each independent variable.
Given a normal or Gaussian function for the sum of variables x and y
z = x~y
(2.17)
where x and y are distributed normally with
Oz Oz
Ox
and ~ and ~ are standard deviations of x and y substituted into Eq. (2.16)
~2
~2
~2
Z z ~ Z x + 2y
The Gaussian function for the product of variables x and y
z=xy
where
Oz
(2.19)
Ox Y’
--:Xoy
with the means px and #y substituted with ~x and~ythe standard deviations
into Eq. (2.16)
~2
2~2 2 2
(2.20)
Z z ~yZx’q-~xZy
The division of variables x and y
X
z=(2.21)
Y
where
Oz 1
Oz
x
Ox y’ Oy
y2
and again the means substituted for x and y and ~x and~y substituted into