Relative frequencies
... exact formulation I shall examine in Part III below. But his book appeared in 1934, too early to be addressed to Kolmogorov's mathematical theory (which appeared in 1933), and much too early to guess that the latter would become the standard basis for all work in the subject. So Borel fields and cou ...
... exact formulation I shall examine in Part III below. But his book appeared in 1934, too early to be addressed to Kolmogorov's mathematical theory (which appeared in 1933), and much too early to guess that the latter would become the standard basis for all work in the subject. So Borel fields and cou ...
4 Combinatorics and Probability
... For each of the n! possible sorted orders, either X is less than Y or it is not. Thus, the n! possible orders are divided into two groups, those for which the answer to the first test is “yes” and those for which it is “no.” One of these groups must have at least n!/2 members. For if both groups hav ...
... For each of the n! possible sorted orders, either X is less than Y or it is not. Thus, the n! possible orders are divided into two groups, those for which the answer to the first test is “yes” and those for which it is “no.” One of these groups must have at least n!/2 members. For if both groups hav ...
CHAPTER III - MARKOV CHAINS 1. General Theory of Markov
... (c) If λ ∈ C is a root of the characteristic polynomial of T different from r then |λ| < r. (d) The eigenvector of T for r can be chosen so that all its entries are strictly positive. Proof. We first construct an eigenvector for T with all positive entries. To do this let S be the set ...
... (c) If λ ∈ C is a root of the characteristic polynomial of T different from r then |λ| < r. (d) The eigenvector of T for r can be chosen so that all its entries are strictly positive. Proof. We first construct an eigenvector for T with all positive entries. To do this let S be the set ...
