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probability generating functions

c0nor · 2012-04-21 17:57:43

Hello. Just a concept I'm failing to get to grips with. A theorem states: let X1,X2... be independent and identically distributed random variables with pgf Gx(s). Let N have pgf GN(S). Then z = X1 + X2... +Xn, a sum of a random number of random variables, has pgf Gz(s) = GN(Gx(s)) Why is Gz(s) = GN(Gx(s))? Should Gz(s) not…

21-04-2012 5:57pm

#1

c0nor

Registered Users, Registered Users 2 Posts: 28 ✭

Join Date: August 2008

Posts: 17

Hello. Just a concept I'm failing to get to grips with. A theorem states: let X1,X2... be independent and identically distributed random variables with pgf Gx(s). Let N have pgf GN(S). Then z = X1 + X2... +Xn, a sum of a random
number of random variables, has pgf Gz(s) = GN(Gx(s))

Why is Gz(s) = GN(Gx(s))? Should Gz(s) not equal the product of the pgf's from X1 to Xn? Any thoughts welcome!

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