The probability distribution is $\displaystyle {1 \over 6}$ for k=1,2,3,4,5,6.

But what is its generating function?

Can anyone explain why it is $\displaystyle { {s+s^2+s^3+s^4+s^5+s^6} \over {6}}$

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- Dec 22nd 2007, 02:43 AMchopetProb distribution of a throw of the die
The probability distribution is $\displaystyle {1 \over 6}$ for k=1,2,3,4,5,6.

But what is its generating function?

Can anyone explain why it is $\displaystyle { {s+s^2+s^3+s^4+s^5+s^6} \over {6}}$ - Dec 22nd 2007, 02:53 AMchopet
Got it.

We shold not be fixated in the form of s but rather its coefficients.

To generate the coefficients of 1,1,1,1,1,1, the generating function is:

$\displaystyle {{s (1-s^6)} \over {1-s} } = s+s^2+s^3+s^4+s^5+s^6 $

Thanks for reading. - Dec 22nd 2007, 03:16 AMCaptainBlack
It is this by definition of the probability generating function of the distribution.

Why this is a useful definition is another mater, and the answer to that is

its usefully properties (you should also note that it encapsulates all the

information in the pmf). Some of the properties that are of use can be found

here.

You should note that this is a z-transform of the pmf, which is the

discrete analogue of the Laplace transform, which of course with a bit

of jiggery-pokery gives the moment generating function for a continuous

distribution.

RonL