Abstract
When one speaks of a uniform distribution if, in the arithmetical case, each point of the label set carries the same probability value and, in the geometrical case, if the probability density is constant for all points x of the label set. This chapter discusses the simple operations that are applicable to collectives with uniform arithmetical distribution. It reviews Bernoulli problem and related questions. One of the most impressive applications of elementary probability calculus is to the theory of heredity. The chapter discusses application of elementary probability calculus to Mendelian heredity theory. Markov chains deal with the most immediate generalization of independent trials, a particular form of dependence. In this, the original variable x can take on any finite number r of values, or countably many, or it may even be continuous. Markov chains have been extensively and systematically investigated and are of great interest, both theoretically and from the point of view of applications. The chapter presents a few explanations and examples concerning finite Markov chains with constant transition probabilities.
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