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Statistics Expnential Help Required

Hi there,

So I am studying an econometric theory module at university and have came across something (which I feel is) confusing. My lecturer is on holiday atm and can't be got hold of.

So anyway, I understand the function of an exponential to be:


But in a past paper he has wrote it as:
(e^(-x/ μ))/ μ

It is in relation to working out the moment generating function, is this just a simple a re-arrangement or something else?

Any help would be greatly appriciated!

Thanks in advance
Original post by Easy_A
Hi there,

So I am studying an econometric theory module at university and have came across something (which I feel is) confusing. My lecturer is on holiday atm and can't be got hold of.

So anyway, I understand the function of an exponential to be:


But in a past paper he has wrote it as:
(e^(-x/ μ))/ μ

It is in relation to working out the moment generating function, is this just a simple a re-arrangement or something else?

Any help would be greatly appriciated!

Thanks in advance


So the PDF of an exponential distribution is definitely λe−λx\lambda e^{-\lambda x}. I'm not sure why he has written it in that form. :s-smilie:

To work out the MGF, you need to calculate: E[etx]=∫0∞etxλe−λxdxE[e^{tx}]=\int_{0}^{\infty }e^{tx}\lambda e^{-\lambda x}dx

There is a nice trick that you can use which means you can do this without actually preforming any integration. :smile:
(edited 9 years ago)
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Easy_A
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Original post by rayquaza17
So the PDF of an exponential distribution is definitely λe−λx\lambda e^{-\lambda x}. I'm not sure why he has written it in that form. :s-smilie:

To work out the MGF, you need to calculate: E[etx]=∫0∞etxλe−λxdxE[e^{tx}]=\int_{0}^{\infty }e^{tx}\lambda e^{-\lambda x}dx

There is a nice trick that you can use which means you can do this without actually preforming any integration. :smile:


Yeah me neither and thanks!

Original post by Farhan.Hanif93
In the specific past paper example, λ=1μ\lambda = \dfrac{1}{\mu}.

Ahh, that makes sense, so I just sub 1/mu for lambda

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