I used to know how but now I forgot.
I want to be able to solve this question:
Let M(t) be the m.g.f. of a Poisson random variable, and define R(t)=ln M(t). Using R(t) find the mean and variance of the Poisson distribution.
So M(t)= e^[lambda*(e^t-1)] and then taking the ln of that only the exponent remains. I feel like I need to plug in t=0 somewhere along the line but then I would be left with lambda times zero when the mean and variance should both equal lambda
I want to be able to solve this question:
Let M(t) be the m.g.f. of a Poisson random variable, and define R(t)=ln M(t). Using R(t) find the mean and variance of the Poisson distribution.
So M(t)= e^[lambda*(e^t-1)] and then taking the ln of that only the exponent remains. I feel like I need to plug in t=0 somewhere along the line but then I would be left with lambda times zero when the mean and variance should both equal lambda
How do I find mean and variance using natural log of moment generating function?
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