Let A1, A2, and A3 be events with probabilities 1/5, 1/4, and 1/3, respectively. Let N be the number of these events that occur.

a) Write down a formula for N in terms of indicators.

b) Find E(N)

In each of the following cases, calculate Var(N):

c) A1, A2, A3 are disjoint;

d)they are independent;

e) A1 is a subset of A2 is subset of A3.