In the two-period economy illustrated in Figs. 2.1 and 2.2 consider an asset paying a dividend at time 2 given by D2 =

⎧

⎪⎨

⎪⎩

0, for ω = 3, 5, for ω ∈ {1, 2, 4}, 10, for ω ∈ {5, 6}.

(a) What is the expectation at time 0 of D2? What is the expectation at time 1 of D2?

Verify that the Law of Iterated Expectations holds for these expectations.

(b) What is the variance at time 0 of D2? What is the variance at time 1 of D2? Confirm that Var[D2] = E [Var1[D2]] + Var[E1[D2]].