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Hi, having touble with this moment generating function problem.

I'm given the moment generating function $M_X(t)=\frac {a} {3e^{-t}-2}$ and need to find $a$ and the largest admissible domain for $M_X(.)$.

I know that $M_x(t) = E(e^{tX}) = 1 + tm_1 + \frac{t^2m_2}{2!} + \frac{t^3m_3}{3!} + \ldots +\frac{t^nm_n}{n!} + \ldots$m where $m_n$ is the $n$th moment.

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Note that $M_x(0)=1$. What does this tell you about $a$? – joriki Nov 2 '12 at 1:48

We have $$M_X(t)=\frac{a}{3e^{-t}-2}=c_0+c_1 t+c_2 t^2+\cdots,$$ so $M_X(0)=a=c_0$. You know what $c_0$ needs to be.

For your second question, what $t$ gives $3e^{-t}-2=0$?

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