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STA4321HW1

STA4321HW1 - STA 4321 Introduction to Probability Theory...

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STA 4321 I ntroduction to P robability T heory Assignment 1 Assigned Wednesday January 13 Due Wednesday January 20 Show your work to receive full credit. 1. Let A 1 , A 2 , . . . be a countable collection of sets. Give a formal proof (not a picture) of the following statements. (a) T i =1 A i = S i =1 A i (b) T n i =1 A i = S n i =1 A i (c) A 1 A 2 = A 1 A 2 2. Let A and B be arbitrary events. Use the axioms of probability to prove that P ( A B ) = P ( A ) + P ( B ) - P ( A B ) . [Hint: Note that A B =( A B ) ( A B ) ( B A ) and A B, A B and B A are disjoint events.] Be sure to specifiy where exactly the axioms of probability are used. 3. Let A be an arbitrary event. Use the axioms of probability to prove that P ( A ) = 1 - P ( A ) . STA 4321 - Introduction to Probability Theory Spring 2010 1 Jorge Rom´an

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STA 4321 4. Roulette is a casino and gambling game named after a French diminutive for “little wheel.” In the game, players may choose to place bets on either a number, a range of numbers, the colors red or black, or whether the number is odd or even. There are 18
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STA4321HW1 - STA 4321 Introduction to Probability Theory...

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