a random variable has generating function g(s)=(3-2s^3)^(-1). how to calcula
te p(X=2) and p(X=3). thanks very much.
s*********n 发帖数: 237
2
?moment generation function? g(0)!=1?
p*****k 发帖数: 318
3
it's the prob generating function, as g(1)=1
just do Taylor expansion and get the coefficients:
g(s) = (1/3) * (1-2s^3/3)^(-1) = (1/3) * (1 + 2s^3/3 + 4s^6/9 + ...)
so p(X=2)=0 and p(X=3)=2/9
