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02fin - Statistics 134 Fall 2002 FINAL EXAM Name SID number...

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Statistics 134, Fall 2002 Prof. Pitman FINAL EXAM Name: SID number: SHOW CALCULATIONS, OR GIVE REASONS, ON ALL PARTS OF ALL QUESTIONS. DO NOT LEAVE NUMERICAL ANSWERS UNSIMPLIFIED. You may refer to your text and class materials. 1 2 3 4 5 6 7 8 9 10 Total

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1. Each time a random number generator is run, it produces a pair of digits by making two draws at random with replacement from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The generator is run 5000 times. Let X be the number of times it produces the pair 00. Find an integer n so that P ( X n ) is approximately 85%.
2. A standard deck consists of fifty-two cards. Four of the cards are aces. Cards are dealt from the deck at random without replacement until two aces have appeared. Let X 1 be the number of cards dealt till the first ace appears. Let X 2 be the total number of cards dealt till the second ace appears. So P ( X 2 > X 1 ) = 1. a) Find P ( X 1 = 1 , X 2 = 5). b) Find P ( X 1 = 1 | X 2 = 5).

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3. I have three painted dice.
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