## Generation and testing of pseudo-random numbers |

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### Contents

LIST OF TABLES Page | 3 |

NUMBER THEORETIC RESULTS | 7 |

STATISTICAL CONSIDERATIONS | 25 |

6 other sections not shown

### Common terms and phrases

15 sets 2n digit 2P divides an-l anxQ mod approximation arithmetic attain aXjj binomial coefficient chi-square test Chinese Remainder Theorem conclude congruence relation congruential and mixed contrary to assumption customary to take defined by taking distributed on 0,1 distributed random numbers distributed random variable divisible by 2P expression full period hence higher order bits Ifex implies integer Jfl)c length of period machines of word Maclarin maximum period mid-square method minimal exponent mixed congruential method mod 2P Monte Carlo method multiplicative congruential method Neumann normally distributed normally distributed random number theoretic properties numbers satisfying parameters prime factor prime power factors primitive root produce random pseudo-random random digits relatively prime runs of length satisfies 11 sequences of numbers serial correlation smallest exponent standard deviation statistical tests subinterval successive pairs term random test on 15 test on successive tial method uniformly distributed random unit interval unit square