Testing a random number generator Run a program generating a uniform random number U(0,1]1000 times calling a success if the value is greater than 1. Determine the number of successes. E.g 520 successes. Repeat the above 500 times; there will be 500 values. The theoretical distribution of the 500 values is a binomial distribution and probability of having i successes (p), i=0,1,...,1000 is C(1000,i)*(2)1 1000 This is hard to calculate for any i. Instead a good approximation is a normal distribution with mean 500 and standard deviation of o=sqrt(n*p*(1-p)= sqrt(1000/4)=15.8. Then under the null hypothesis 95% of the points will be between 468 and 531 (mean+/- 20). If 95%of the number of experimental values are within these limits, we accept that the random number generator is good. Run a program to check.

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