Let X have a Poisson distribution with parameter L(short for lambda here )
show that the MGF function of Y=(x-L)/sqrt(L) is given by
m(t) = exp(lamda*e^(t/sqrt(lamda)) - sqrt(lamda)t - lamda)
Here's what I did:
My(t)=E(e^Yt) =E[e^(t(x-L)/sqrt(L))] =and some more expansion, so what now ? I've read wiki and wolfmen already.