2. THE SLOPE OF THE NUMBER COUNTS OF RADIO SOURCES. 2. The distribution of flux densities of extragalactic radio sources are distrib power-law with slope -o, say. In a non-evolving Euclidean universe o = 3/2 prove this?) and departure of a from the value 3/2 is evidence for cosmological of radio sources. This was the most telling argument against the steady-state c in the early 1960s (even though they got the value of a wrong by quite a long w Given error-free observations of radio sources with flux densities Sqi = 1, ... a known, fixed measurement limit So, what is the posterior for a? What is (maximum a posteriori) value of a? If a single source is observed with flux $1 = 250, what is the most probable va Can you deduce the uncertainty on a? Hints: 1. You will use the distribution as a probability distribution function (pdf), p(S) have to normalise it. 2. A pdf is not a probability, but p(S) AS is, for a (small) interval AS. You wil introduce an arbitrary (but small) interval around each source