p ( x ) –the prior distribution, p ( x y o ) –the posterior distribution, and p ( y o x –the likelihood function, are plotted in figure 1 for four different values for y o . A unique property of the Gaussian pdfs can be seen in them, and in
the above equations: the shape of the posterior distribution,and its relative position to x b and o , are both independent of
the observed value. They only depend on the error variances.