I am learning auto-correlation function for fluorescence correlation spectroscopy (FCS) on fcsXpert.com. The web page says:
For random processes such as diffusion, the average of the square of the fluctuations in a parameter equals the average parameter value.
To provide some context to this problem: in FCS, a sub-micrometer size volume in a dilute solution is illuminated with light. The solute molecules tagged with fluorescent probes diffuse across the small illuminated volume, emitting light signals upon being excited. The fluctuations to the intensity signals as the time passes are analysed using auto-correlation function. As expected, random diffusion contributes to the fluctuations to the average number of tagged molecules in the illumination volume, hence also to the fluctuations in light intensity. The question I have is:
why is the sample variance to the average molecule number in the small volume equal to the average molecule number, for random diffusion process?
Please correct me if I actually have understood the text incorrectly. Thanks!