1. According to the fundamental assumption of statistical thermodynamics, the probability P(N, S) for a large N binary magnet system with spin excess 2s is given by P(N, s) = (/2 exp(-2). (a) Plot P(N,s) for N = 10, 1000, and 100000: In order to appreciate the very nature of Gaussian statistics, you need to plot P(N,s) for |s| N/2. N N 202. (b) The Gaussian standard deviation of a Gaussian distribution- exp(- is parametrized by . Therefore, o of P(N,s) is N/2. Show that o = ((s-(s))) = (s) - (s) = N/4 by direct calculation. (c) How is o related to the full width half maximum (FWHM)? 1