6.20 () (f) Find the second moment for a Poisson random variable by using the characteristic function results shown in Table 6.1.Values PMF E[X] var (X ) Px (w) Uniform M(M+1) sin [(2M +1)w/2] k= -M....,M O 2M +1 3 (2M+1) sin[w /2] Bernoulli k=0,1 p* ( 1 - p) 1 - k P p(1 - p) pexp(jw)+ (1-p) Binomial k=0,1,...,M (K ) ph ( 1 - p) M - k Mp Mp(1 - p) [pexp(jw) + (1-p)]M Geometric k=1,2 , ... (1 - p)k-1p P exp(-jw) -(1-p) Poisson k=0,1 , ... exp (-1)k K ! A exp[X( exp(jw) -1)] Table 6.1: Properties of discrete random variables