5. How would you generate a random sample from the statistical distribution given in the following diagram: 4 ·X ? 2 In other words, how would you generate a sequence of integers {0, 1, 2} where 0 and 2 have probability of .25 and 1 has a probability of .5? 1|2

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Hi!  Homeschool mom here asking for help on the question highlighted on the image.  Textbook is by Stanley Farlow, Partial Differential Equations for Scientists and Engineers. Chapter title: Monte Carlo methods (an introduction).  The question ask, "how would you generate a random sample...how would you generate a sequence of integers?"  

5. How would you generate a random sample from the statistical distribution
given in the following diagram:
1
4
4
-X ?
0
1
2
In other words, how would you generate a sequence of integers {0, 1, 2}
where 0 and 2 have probability of .25 and 1 has a probability of .5?
6. The Buffon needle problem says that a needle (of length one) tossed ran-
domly on the American flag (the width of the red and white stripes is also
one) has a probability of 2/T of crossing one of the lines between the stripes.
How would you design a game (and computer program) to evaluate ?
OTHER READING
Monte Carlo Methods by J. M. Hammersley and D. C. Handscomb. Methuen and Com-
pany (London), 1964. This concise book outlines the general principles of the Monte
Carlo method. Solutions of differential equations, eigenvalue problems, and integral
equations are given in addition to problems in statistical mechanics, neutron diffusion,
and radiation shielding. The book also contains many additional references.
Monte Carlo Methods (an Introduction) 345
1|2
Transcribed Image Text:5. How would you generate a random sample from the statistical distribution given in the following diagram: 1 4 4 -X ? 0 1 2 In other words, how would you generate a sequence of integers {0, 1, 2} where 0 and 2 have probability of .25 and 1 has a probability of .5? 6. The Buffon needle problem says that a needle (of length one) tossed ran- domly on the American flag (the width of the red and white stripes is also one) has a probability of 2/T of crossing one of the lines between the stripes. How would you design a game (and computer program) to evaluate ? OTHER READING Monte Carlo Methods by J. M. Hammersley and D. C. Handscomb. Methuen and Com- pany (London), 1964. This concise book outlines the general principles of the Monte Carlo method. Solutions of differential equations, eigenvalue problems, and integral equations are given in addition to problems in statistical mechanics, neutron diffusion, and radiation shielding. The book also contains many additional references. Monte Carlo Methods (an Introduction) 345 1|2
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