The photons or the quantum of energy, as a natural phenomenon with too large population, must have a natural behavior. Therefore, the quanta of energy, like many random variables that occur in nature, behave as though their distribution is normal or approximately normal. Because of this, here we use the Normal, or Gaussian, Distribution Law in the probability theory as our mathematical model in which the random variable is the energy of photon.
This analysis shows us what has been known (measured) as the speed-of-light limit (c = 300,000km/s) is the speed of those photons having an energy very close to the mean value. Because, Ē is a Mathematical Expectation only and it never happens.