Where do random numbers come from?
Most of us already have an intuitive notion of what random numbers are, but, as we’ll see, this is a difficult question to answer precisely. Simply said, we should not be able to use the numbers that we have seen to predict which number will come next or to restrict the possibilities. For example, you may wish to think of rolling an ideal die. On each roll, each of the numbers–1, 2, 3, 4, 5, 6–is equally likely to appear. If we roll many times, we may expect to see each of the six possibilities roughly one-sixth of the time. In addition, if we count the number of successive pairs, we would expect to see each of the 36 possible pairs appear with roughly equal frequency. It is possible, however, that we roll the die one thousand times and obtain a “1” each time. Regardless, each number is equally likely to show up on the 1001st time. (This seeming paradox lies behind a well known Dilbert cartoon.) At first glance, it may seem like a simple thing to generate random numbers. In fact, you
