MA519_AUG03

# MA519_AUG03 - QUALIFYING EXAMINATION AUGUST 2003 MATH 519 -...

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QUALIFYING EXAMINATION AUGUST 2003 MATH 519 - Prof. Eremenko NAME: 1. An engine of certain type fails with probability p .A nr o c k e th a v i n g several engines of this type crashes when at least half of its engines fail, and they fail independently of each other. Suppose that two such rockets, one with two engines and another with four engines, have the same probability of crash. Find p . 2. Let X 1 ,X 2 ,X 3 and X 4 be independent uniformly distributed points on a circle. What is the probability that the chords [ X 1 ,X 2 ]and[ X 3 ,X 4 ] intersect. 3. A ball of radius R contains N random points which are independently and uniformly distributed. a) Find the distribution of the distance from the center to the closest point. b) Find the limit of this distribution when N/R 3 4 πλ/ 3, where

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MA519_AUG03 - QUALIFYING EXAMINATION AUGUST 2003 MATH 519 -...

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