prob.part5.11_12 - 1.1. SIMULATION OF DISCRETE...

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Unformatted text preview: 1.1. SIMULATION OF DISCRETE PROBABILITIES 3 .203309 .762057 .151121 .623868 .932052 .415178 .716719 .967412 .069664 .670982 .352320 .049723 .750216 .784810 .089734 .966730 .946708 .380365 .027381 .900794 Table 1.1: Sample output of the program RandomNumbers . Let X be a random variable with distribution function m ( ω ), where ω is in the set { ω 1 , ω 2 , ω 3 } , and m ( ω 1 ) = 1 / 2, m ( ω 2 ) = 1 / 3, and m ( ω 3 ) = 1 / 6. If our computer package can return a random integer in the set { 1 , 2 , ..., 6 } , then we simply ask it to do so, and make 1, 2, and 3 correspond to ω 1 , 4 and 5 correspond to ω 2 , and 6 correspond to ω 3 . If our computer package returns a random real number r in the interval (0 , 1), then the expression 6 r + 1 will be a random integer between 1 and 6. (The notation x means the greatest integer not exceeding x , and is read “floor of x .”) The method by which random real numbers are generated on a computer is described in the historical discussion at the end of this section. The following example gives sample output of the program RandomNumbers . Example 1.1 (Random Number Generation) The program RandomNumbers generates n random real numbers in the interval [0 , 1], where n is chosen by the user. When we ran the program with n = 20, we obtained the data shown in Table 1.1....
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prob.part5.11_12 - 1.1. SIMULATION OF DISCRETE...

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