Polya’s urn model supposes that an urn initially contains r red and b blue balls. At each stage a ball is randomly selected from the urn and is then returned along
with m other balls of the same color. Let Xk be the number of red balls drawn in
the first k selections.
(a) Find E[X1].
(b) Find E[X2].
(c) Find E[X3].
(d) Conjecture the value of E[Xk], and then verify your conjecture by a conditioning
argument.