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 colour. Let Xk be the number of red balls drawn in the rst k selections.

(a) Find E(X1).

(b) Find E(X2).

(c) Conjecture the value of E(Xk), and then verify your conjecture by a conditioningargument