Question: Problem 5. In this problem, you may need to use the following so-colled inclusion-exclusion principle without proof. Let A1,A2, - -- ,An be n events.

ZIP(Ai) Z 1P(Am Aj) i=1 1gi k), k=0 show that (3-ii) Consider

E[T] as a function of N. Show that [T]~ V TN 2

as N -+ 0o. Here the notation an ~ by means limN

Problem 5. In this problem, you may need to use the following so-colled inclusion-exclusion principle without proof. Let A1,A2, - -- ,An be n events. Then it IP(A1 u . . . u An) = ZIP(Ai) Z 1P(Am Aj) i=1 1gi k), k=0 show that (3-ii) Consider E[T] as a function of N. Show that [T]~ V TN 2 as N -+ 0o. Here the notation an ~ by means limN -to by an = 1. Hint: Try to use the central limit theorem in a suitable context.]

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