Let's say I have this random variable $X$ with $E(X)=\mu$ and $Var(X)=\sigma^2$. How can I find the moment generating function? I know that $M'(0)=E(X)$, and that in general $M^{(k)}(0)=E(X^k)$. So I'd force $M'(0)=\mu$ and that $M''(0)=E(X^2)=\sigma^2+\mu^2$. How can I proceed?
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You have not been given enough information to find the generating function. You will likely need more information , such as the distribution of $X$. – Sarvesh Ravichandran Iyer Jan 16 '22 at 16:42
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That's true I missed an information. X has normal distribution. so? – Cristie Jan 16 '22 at 16:55
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1Ah, in that case, you might want to look here. Your formulas are right, but constructing the moment generating function from the derivatives to get an explicit formula is quite difficult. – Sarvesh Ravichandran Iyer Jan 16 '22 at 16:56
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Oh, great! Thank you, you have been precious! – Cristie Jan 16 '22 at 17:00
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You're welcome, I will now close this as a duplicate of the attached question. – Sarvesh Ravichandran Iyer Jan 16 '22 at 17:02