A memoryless information source has a countably infinite symbol alphabet S = {S1, S2,...} with P = ba for i=1,2,.... Express b in terms of a. (b) Calculate the entropy of S as a function of a. Hint: a = a and 1 ia = (1-) given |a| 1. i=1 (5 marks) (5 marks) (Total 10 marks) Question: In the absence of sources, steady convection and diffusion of a o in a given one-dimensional flow field u is governed by d/dx(pup) = d/dx(rd/dx). A property p is transported by means of convection and diffusion through the one-dimensional domain. The governing equation is (5.1); the boundary conditions are p(0) = 1 at x = 0 and p(L) = 0 at x = L. Using five equally spaced cells and the power law differencing scheme for convection and diffusion, calculate the distribution of as a function of x for (i) Case 1: u = 0.1 m/s, (ii) Case 2: u = 2.5 m/s, (5.1) where length L = 1.0 m, p = 1.0 kg/m3, [= 0.1 kg/m.s.