Example class 3

Example class 3 - Department of Statistics and Actuarial...

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Department of Statistics and Actuarial Science STAT1301 Probability and Statistics I Example Class 3 1. Two numbers are successively selected at random and with replacement from the set f 1 ; 2 ; ; 100 g . What is the probability that the rst one is greater than the second? answer: suppose the rst number is X and the second number is Y , then P ( X < Y ) + P ( X > Y ) + P ( X = Y ) = 1 ; P ( X < Y ) = P ( X > Y ) and we know that P ( X = Y ) = 100 10000 thus P ( X > Y ) = 1 ¡ 100 10000 2 = 99 200 2. Let A 1 ; A 2 ; ; A n be n events. Show that if P ( A 1 ) = P ( A 2 ) = = P ( A n ) = 1, then P ( A 1 \ A 2 \ A n ) = 1. answer: P ( T n i =1 A i ) = 1 P (( T n i =1 A i ) c ) = 1 P ( S n i =1 A c i ) 1 P n i =1 P ( A c i ) = 1 3. Suppose That 20 sticks are broken each into one long and one short part. By pairing them randomly, the 40 parts are then used to make 20 new sticks. What is the probability that long parts are all paired with short ones? What is the probability that the new sticks are exactly the
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This note was uploaded on 04/29/2010 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

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Example class 3 - Department of Statistics and Actuarial...

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