1. The problem statement, all variables and given/known data Let X,W,Y be iid with a common geometric density f_x(x)= p(1-p)^x for x nonnegative integer and p is in the interval (0,1) What is the characteristic function of A= X-2W+3Y ? Determine the family of the conditional distribution of X given X+W? 2. Relevant equations the characteristic function of the geomtric series is p/[1-(1-p)exp(it)] 3. The attempt at a solution The characteristic function of a sum of random variables is the product of the individual characteristic functions. So I need to find the characteristic function of X , -2W and 3Y and multiply them together?