What applications does this knowledge have?
There are many different sources of noise in images with different distributions. For example shot noise, which is a large contributor in low light arises from the random emission of photons follows the poisson distribution. Dark current noise and read noise (major contributions in shadow noise in good light) are more complex as they exhibit banding and are rarely evenly distributed.
Regarding applications of this knowledge, most commercial noise reduction software works by fitting a distribution to the image data by finding an area of constant colour (either automatically or by user intervention) to estimate the parameters of the distribution so knowing these values in advance is not important.