Let A1, A2 and A3 be events with probabilities 1/5, 1/4, 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 in A2 is in A3.