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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.

user1919987
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  • See http://en.wikipedia.org/wiki/Law_of_the_unconscious_statistician – JessicaK Jan 30 '15 at 01:36
  • I tried , but still cant get the form right – user1919987 Jan 30 '15 at 01:53
  • Use the Law of the unconscious statistician, factor out all terms that do not involve your summation index, rewrite the series into the form of the series for $e^{x}$ and replace the series with the exponential. – JessicaK Jan 30 '15 at 02:05

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