Question 5 (ross 1.6): Show that E (FUG) = EF U EG MGMT9

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    Question 5 (ross 1.6): Show that E (FUG) = EF U EG
    MGMT901 PROBABILITY THEORY & STATISTICS Homework Assignment 1 Assigned on October 1 Due on October 8 1. Miller and Miller 1.30 2. Miller and Miller 1.44 3. A probability space consists of three parts: (a) A sample space S which is the set of all possible outcomes. (b) A set of events F where each event is a set containing zero or more outcomes. (c) A function P that assigns probabilities to the events. Hence (S;F; P) denotes a probability space. Recall the third axiom of probability: If (any sequence of events) E1;E2; : : : are pairwise disjoint (i.e. mutually exclusive) then P [ 1?i=1Ei] =S1 i=1 P(Ei): Now consider a more general setting where the events in a probability space (S;F; P) are not necessarily pairwise disjoint. For any sequence of events E1;E2; : : : 2 S show that P [ ?n i=1Ei] Sn i=1 P(Ei): 4. Show that P [ ?n i=1Ei] = Sn i=1 (??1)i+1 S 1k1

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