Normalizing the Probability Function
In the above graph the blue line represents the function. We can integrate
the function from negative infiniti to infiniti to determine the area
under the curve. Let's assume this comes to the number 250.
(see the graph above.)
If integrating the function from 'squiggle' to 'squiggle + delta squiggle'
produces the number 125 (see the graph above),
, which corresponds to the area in green under the
function, then we can say that the probability of the value falling on
the range squiggle to squiggle + delta squiggle is 125/250 = 0.5, or 50%.
If you do this procedure to a function f(x) that is already normalized,
then the integration from negative infiniti to infiniti will produce
1. Since we know that integration of P(squiggle) from negative infiniti
to infiniti yields 250, we can define a new function
P(squiggle)
Pnorm = -----------
250
The integration of Pnorm from squiggle to squiggle + delta squiggle will
produce 0.5. From this you can see that we normalize a probability function
so that the answer will tell us what percent of the total probably falls on
the range of our interest.
Last Update- September 3, 1995- wld
is the probability of of finding the value
when
measurements have been taken.
