# Generating functions

• Jan 8th 2009, 10:56 AM
math_lete
Generating functions
Hi can anybody help?
I am revising generating functions and came across the question.
A player can score 0,1 or 2 points in a game with respective probabilities 1/10,3/5 and 3/10. A sequence of n independent games is played, where n is the value obtained by throwing a fair die. Find the PGF of the total sun of scores obtained by the player and the expectation of the total sum.

In the example they start off by working out GN(s) as equal to
s(1-s^6)/6(1-s). I do not understand how they have got to this. Can anybody help? I am also stuggling with working out the expectation.
Thanks
• Jan 8th 2009, 11:42 AM
Moo
Hello,

The expectation is defined as :
$\lim_{t \to 1} g_n'(t)$

But I'm thinking on how they got the generating function (Surprised)
• Jan 8th 2009, 11:46 AM
math_lete
thanks yeh i think it may be some kind of power series?
• Jan 8th 2009, 11:50 AM
Moo
Quote:

Originally Posted by math_lete
thanks yeh i think it may be some kind of power series?

It has to !

I was struggling with finding the sum of scores...

Here are some of my thoughts.
Let S be the sum of scores obtained during the n games.

S can vary from 0 (n times 0) to 2n.
Now you have to find the probability that P(S=k), where k is an integer between 0 and 2n.
Maybe you know some methods, but I can't remember if I've learnt one ><