HW03 Answers - Solution for 36217 Wanjie Wang Teacher...

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Unformatted text preview: Solution for 36217 Wanjie Wang Teacher: Jiashun Jin September 19, 2009 If there is any question, please contact me at [email protected] 1. 10 Points With Bayes’ Rule, P (the k th coin | heads) = P ( the k th coin and heads ) P n 1 P ( heads | the k th coin ) P ( the k th coin ) = i/n × 1 /n P n 1 i/n × 1 /n = i/n 2 ( n +1) / 2 n = 2 i n ( n +1) 2. 10 Points Define the event B= { Beppe has been pardoned } , C= { Carlo has been pardoned } . P(A)=P(B)=P(C)=1/3. If A happens, the probability for the warden to tell him Beppe will be executed is 1/2. If C happens, the probability for the warden to tell him Beppe will be executed is 1. With the assumption, P(B)=0. With Bayes’ Rule, P ( A | W ) = P ( W | A ) P ( A ) P ( W | A ) P ( A )+ P ( W | B ) P ( B )+ P ( W | C ) P ( C ) = 1 / 2 × 1 / 3 1 / 2 × 1 / 3+0+1 × 1 / 3 = 1 / 3 3. 10 Points To find partitions of 40 into 4 parts, imagine that we have 40 items in a line, and three markers 1, 2, 3. We put the markers between arbitrary two items, but keepthree markers 1, 2, 3....
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This note was uploaded on 09/30/2010 for the course STATISTICS 36-217 taught by Professor Jin during the Fall '09 term at Carnegie Mellon.

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HW03 Answers - Solution for 36217 Wanjie Wang Teacher...

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