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Let $X_1, X_2, \cdots X_{k-1}$ have a multinomial distribution. I need to find the mgf of $X_2, \cdots X_{k-1}$. I think it should be \begin{align*} M_{X}(0, t_2, \cdots, t_{k-1})= (p_1+p_{2}e^{t_{2}}+\cdots p_{k}e^{t_k})^{n}. \end{align*}.

I don't know if this is correct or how simple it should be, I have been getting confused about the multinomial mgf. Any explanation appreciated.

mXdX
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    The general form of the moment-generating function is indeed $$\left(\sum_{i=1}^k p_ie^{t_i}\right)^n. $$ Are you having trouble in deriving this expression? – Math1000 Nov 11 '19 at 20:03
  • I am having trouble, I can't seem to find anything helpful online. – mXdX Nov 11 '19 at 21:44
  • See here: https://math.stackexchange.com/questions/2282454/moment-generating-function-of-multinomial-distribution – Math1000 Nov 12 '19 at 01:44
  • Thanks, this is helpful -- I've noticed sometimes people define the mgf as $\sum_{i=1}^{k-1} p_{i}e^{t_{i}}+p_{k}$. Are they equivalent somehow? This is why I was so confused.. – mXdX Nov 12 '19 at 02:32
  • That doesn't seem correct to me. – Math1000 Nov 12 '19 at 02:36
  • Okay. I've also had to work through a typo in my textbook, which didn't help my confusion. Would my answer to the question in the original post be correct, then? – mXdX Nov 12 '19 at 02:40

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