# Expansion of an MGF as a power collection

I have actually been asked to expand (1 - 2t) ^ (- n/2). Until now I have actually located the log of this function and afterwards set apart two times in order to locate my mean and also difference as n and also 2n specifically. Just how do I write my last solution as a power collection in t regarding the term in t ^ 2?

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2019-12-02 02:53:32
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If you intend to expand your function in a power collection on the argument $t$ you can write its Taylor Polynomials.
You have actually currently done a lot of the job. If the mean $\mu'_1$ and also difference $\sigma^2$ amount to $n$ and also $2n$, specifically, after that the 2nd minute $\mu'_2$ is offered by $\mu'_2 = \sigma^2 + (\mu'_1)^2 = n(n+2)$. Currently, the minute - creating function can be increased as adheres to : $$M(t) = 1 + \mu' _1 t + \frac{1}{{2!}}\mu' _2 t^2 + \cdots = 1 + nt + \frac{{n(n + 2)}}{2}t^2 \cdots.$$