... that thestandard deviations σ of these normal distributionsare the same for all points. Thenthe probability of the data set is the product of the probabilities of each point,P ∝Ni=1exp−12yi− ... assumption of a normal distribution.For a hundred years or so, mathematical statisticians have been in love withthe fact that the probability distribution of the sum of a very large number of verysmall ... distribution is often rather poorly realized, if it isrealized at all. We are often taught, rather casually, that, on average, measurementswill fall within ±σ of the true value 68 percent of the time,...