A bag contains N balls split between red and blue. The number of red balls Xo
is a random variable having PMF Po and PGF G0.
A ball is randomly selected from the bag and replaced with a ball of opposite colour (red T
blue). This process is repeated indefinitely. Let Xn be the number of red balls in the bag
after n draws, and Pn and Gn be (respectively) the PMF and PGF of Xn.
(b) By conditioning on Xo, show that
P1 = 1 - x N - 1 - + 1 € R.
(c) Show that
(d) Prove that for any n EN,
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