Consider a Poisson process (e.g., counting radiative decays or counting photons on an Astronomical detector) in which N = 75 and B = 50 counts were recorded. Assuming that the resulting source counts, S = NB, can be approximated as a Gaussian, f(S), and that the covariance TB is negligible, determine (a; 5 pts) S of the distribution and (b; 8 pts) the probability that the source emitted S 20 counts in the collection of N.