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UNM/MPJ CS452/Mgt532 IV. Random Numbers UNM/MPJ CS452/Mgt532 IV. Random Numbers IV. Random Numbers M. Peter Jurkat CS452/Mgt532 Simulation for Managerial Decisions The Robert O. Anderson Schools of Management University of New Mexico Need for Random Numbers To generate values from a statistical distribution Examples: a time interval after the previous arrival (e.g., neg exp), a value of a service time (e.g., uniform), a number of items in an order (e.g., Poisson) Generation of random numbers satisfied this need Informally, random numbers are selections from a statistical distribution Sources of Random Numbers Physical processes Noise in electrical signal generators, background electron scatter (atmospheric, CRT) Advantages: natural, occurs in systems that use random numbers Disadvantage : hard to measure and make into useful sequences, cannot specify distribution ?Existing tables Last digits of phone number, log, sine, etc. tables Advantages: already exist, many in digital form Disadvantages: not really random, hard to use in simulations, cannot specify distribution Sources of Random Numbers ?Digital algorithms Last digits of arithmetic procedure Advantages: can specify distribution, easy to use in computer simulation Disadvantages: not really random (algorithm = deterministic, will repeat sequence (cycles) Preferred method for computer based simulations – long history, well developed Good algorithms have long periods and pass random tests – widely used – known as pseudo-random number generators Definition Formally, common phrases at random, with equal chance, equally likely usually mean uniformly distributed The sequence 12345678901234567890…, retrospectively consists of equally likely single digits – not random since the next digit can be predicted from the previous – successive digits depend on previous one = not independent Therefore, random numbers are defined to be independent samples from a Uniform distribution Either real numbers on [0,1] or integers on [

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