Synopsis: How can computers, which are completely deterministic
machines, generate "random" numbers?

Many computer programming languages today include a function for generating random numbers. This paper presents some background theory in basic probability theory and inferential statistics. We then present a number of empirical tests for analyzing a computer generated sequence of random numbers, and we apply these tests to several popular random number generators.

A treatise on probability theory wouldn't be complete without a number of paradoxes to thoroughly confuse you. Here are a few classic ones.

How to generate random numbers in the range:

r = [0,1) a real value

x = [0,M) a real value

y = [0,M) an integer value

z = [1,M] an integer value

x = [0,M) a real value

y = [0,M) an integer value

z = [1,M] an integer value

How to use the rand() random number generator.

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