Mathematics — Probability · generating-functions-discrete
Problem
Let X1,X2,…,Xn be an independent trials process, with values in {0,1} and mean μ=1/3. Find the ordinary and moment generating functions for the distribution of
(a) S1=X1. Hint: First find X1 explicitly.
(b) S2=X1+X2.
(c) Sn=X1+X2+⋯+Xn.