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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)

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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.

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