| 2 | ∫ r0 e−r2/n r dr = 1 − e−r2/n |
| n |
(4),
or, which is the same thing, the probability of an amplitude greater than r is
e−r2/n
(5).
The accompanying table gives the probabilities of intensities less than the fractions of n named in the first column. For example, the probability of intensity less than n is .6321.
| .05 | .0488 | .80 | .5506 |
| .10 | .0952 | 1.00 | .6321 |
| .20 | .1813 | 1.50 | .7768 |
| .40 | .3296 | 2.00 | .8647 |
| .60 | .4512 | 3.00 | .9502 |
It will be seen that, however great n may be, there is a fair chance of considerable relative fluctuations of intensity in consecutive combinations.
The mean intensity, expressed by
| 2 | ∫ ∞0 e−r2/n · r2 · r dr, |
| n |