COMP SCI
random numbers

# random numbers - Random Numbers-a sequence of numbers is...

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Random Numbers -a sequence of numbers is random if there is no short pattern that can describe it -given a sequence of numbers, can we tell if it is random? -random numbers are useful for : --simulating processes --computer games --computer graphics --testing software --gambling --cryptography -simulations : --if a model is too complex to model exactly --to observe a system's evolution --fun --aquarium screen savers -one cannot provide an arithmetic algorithm to produce sequences of truly random numbers -we can only provide an algorithm to produce numbers having certain statistical properties --frequency of individual numbers --frequency of pairs

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Unformatted text preview: --average distance between recurring numbers--bit transition tests--autocorrelation tests-complicated mathematical functions often fail the statistical test -reasonably fast and good method is the linear congruential method X(n+1) = (aX(n) + b) mod m for certain choices of a,b,m,X(0)-pseudo random values seem random to those who do not know the algorithm-stock option pricing :--buying or selling is called exercising --price to buy or sell the stock is the strike price --last day they can be exercised is the expiry date --options that can be exercised at any time up to expiry date are “American” options...
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