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A sequence X_1, X_2, ... of random variates is called Markov (or Markoff) if, for any n, F(X_n|X_(n-1),X_(n-2),...,X_1)=F(X_n|X_(n-1)), i.e., if the conditional distribution ...

A spectrum containing the real numbers larger than Freiman's constant.

If x takes only nonnegative values, then P(x>=a)<=(<x>)/a. (1) To prove the theorem, write <x> = int_0^inftyxP(x)dx (2) = int_0^axP(x)dx+int_a^inftyxP(x)dx. (3) Since P(x) is ...

The statistical index P_(ME)=(sump_n(q_0+q_n))/(sum(v_0+v_n)), where p_n is the price per unit in period n, q_n is the quantity produced in period n, and v_n=p_nq_n is the ...

If a matrix group is reducible, then it is completely reducible, i.e., if the matrix group is equivalent to the matrix group in which every matrix has the reduced form ...

Every point which can be constructed with a straightedge and compass, and no other points, can be constructed using identical matchsticks (i.e., identical movable line ...

The term "math" is the usual term for "mathematics" used in the United States. In contrast, the term "maths" is used in the United Kingdom.

The term "maths" is the usual term for "mathematics" used in the United Kingdom. In contrast, the term "math" is used in the United States.

Denote the sum of two matrices A and B (of the same dimensions) by C=A+B. The sum is defined by adding entries with the same indices c_(ij)=a_(ij)+b_(ij) over all i and j. ...

Matrix decomposition refers to the transformation of a given matrix (often assumed to be a square matrix) into a given canonical form.