prob.part28.57_58 - 2.1. SIMULATION OF CONTINUOUS...

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2.1. SIMULATION OF CONTINUOUS PROBABILITIES 49 1. To simulate this case, we choose values for x and y from [ - 1 , 1] at random. Then we check whether x 2 + y 2 1. If not, the point M = ( x,y ) lies outside the circle and cannot be the midpoint of any chord, and we ignore it. Oth- erwise, M lies inside the circle and is the midpoint of a unique chord, whose length L is given by the formula: L = 2 ± 1 - ( x 2 + y 2 ) . 2. To simulate this case, we take account of the fact that any rotation of the circle does not change the length of the chord, so we might as well assume in advance that the chord is horizontal. Then we choose r from [ - 1 , 1] at random, and compute the length of the resulting chord with midpoint ( r,π/ 2) by the formula: L = 2 ± 1 - r 2 . 3. To simulate this case, we assume that one endpoint, say B , lies at (1 , 0) (i.e., that β = 0). Then we choose a value for α from [0 , 2 π ] at random and compute the length of the resulting chord, using the Law of Cosines, by the formula: L = 2 - 2 cos α .
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This note was uploaded on 09/15/2009 for the course SCF scf taught by Professor Scf during the Spring '09 term at Indian Institute Of Management, Ahmedabad.

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prob.part28.57_58 - 2.1. SIMULATION OF CONTINUOUS...

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