# Thread: Which distributions have these MGFs?

1. ## Which distributions have these MGFs?

Which distributions have these Moment Generating functions?

M1(t)= (1/256) (1 + e^t) ^ 8

M2(t)= ( e ^ 2t) / [ ( 2 - e^t) ^ 2 ]

M3(t)= (4^ t^ 2) ( e^ 4t )

the numbers after M are subscripts. Does that mean they are 2nd and 3rd derivatives? I'm kinda lost. thank you for any help

2. Originally Posted by Statsnoob2718
Which distributions have these Moment Generating functions?

M1(t)= (1/256) (1 + e^t) ^ 8

M2(t)= ( e ^ 2t) / [ ( 2 - e^t) ^ 2 ]

M3(t)= (4^ t^ 2) ( e^ 4t )

the numbers after M are subscripts. Does that mean they are 2nd and 3rd derivatives? I'm kinda lost. thank you for any help
They are all MGF's. The subscript is merely to distinguish them from each other.

You're expected to look up a table of distributions and try to re-write what you've been given in a form that you can recognise.

The first one can be written as $\left( \frac{1}{2} e^t + \frac{1}{2}\right)^8$.

The second one can be written as $\left( \frac{e^t}{2 - e^t} \right)^2 = \left( \frac{\frac{1}{2}e^t}{1 - \frac{1}{2} e^t} \right)^2$.

The third one can be written as $\exp \left( -4t + (\ln 4) t^2\right)$.

Big hint: The first two are MGF's of well known discrete distributions. The third is a well known continuous distribution. Note that in each case you will be expected to give the value of the relevant parameters of the distribution.

3. Thank you math GOD! This was very helpful!