StatORJune08

# StatORJune08 - Summer 2008 Probability Solve any three...

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Summer 2008 Probability Solve any three problems for a full credit. Indicate below EXACTLY which three problems you have attempted by circling the appropriate numbers: 1 2 3 4 NAME:________________________________________________ SOLAR ID#:___________________________________________ Start your answer on each question sheet. Attach all extra sheets you use to the appropriate sheet. Hand in all question sheets. Time of Exam is from 9AM-12noon

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1. A stick of length 1 is cut into three pieces of lengths X, Y , and Z , with X Y Z . First, the stick of length 1 is cut into two pieces at a randomly chosen point uniformly distributed along its length. Then the smaller of these two sticks is also cut into two pieces at a randomly chosen point uniformly distributed along its length. These two cuts are conducted independently. Find Cov( X,Y ).
2. Let be exponentially distributed with mean 1 X 1 µ ; let be exponentially 2 X distributed with mean 2 ; and let and be independent. Compute for 1 X 2 X ) | Pr( 2 1 2 1 bX X aX X < < < < b a 0 . What happens in the limit as ? b

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Let
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## This note was uploaded on 01/31/2011 for the course AMS 507 taught by Professor Feinberg,e during the Fall '08 term at SUNY Stony Brook.

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StatORJune08 - Summer 2008 Probability Solve any three...

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