# Randomness, Probability, and Statistics

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1 Why probability and statistics?

Is everything on this planet determined by randomness? This question is open to philosophical debate. What is certain is that every day thousands and thousands of engineers, scientists, business persons, manufacturers, and others are using tools from probability and statistics. The theory and practice of probability and statistics were developed during the last century and are still actively being reﬁned and extended. In this book we will introduce the basic notions and ideas, and in this ﬁrst chapter we present a diverse collection of examples where randomness plays a role.

1.1 Biometry: iris recognition
Biometry is the art of identifying a person on the basis of his or her personal biological characteristics, such as ﬁngerprints or voice. From recent research it appears that with the human iris one can beat all existing automatic human identiﬁcation systems. Iris recognition technology is based on the visible qualities of the iris. It converts these—via a video camera—into an “iris code” consisting of just 2048 bits. This is done in such a way that the code is hardly sensitive to the size of the iris or the size of the pupil. However, at diﬀerent times and diﬀerent places the iris code of the same person will not be exactly the same. Thus one has to allow for a certain percentage of mismatching bits when identifying a person. In fact, the system allows about 34% mismatches! How can this lead to a reliable identiﬁcation system? The miracle is that different persons have very diﬀerent irides. In particular, over a large collection of diﬀerent irides the code bits take the values 0 and 1 about half of the time. But that is certainly not suﬃcient: if one bit would determine the other 2047, then we could only distinguish two persons. In other words, single bits may be random, but the correlation between bits is also crucial (we will discuss correlation at length in Chapter 10). John Daugman who has developed the iris

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