Search Results for ""

Apply Markov's inequality with a=k^2 to obtain P[(x-mu)^2>=k^2]<=(<(x-mu)^2>)/(k^2)=(sigma^2)/(k^2). (1) Therefore, if a random variable x has a finite mean mu and finite ...

The chi distribution with n degrees of freedom is the distribution followed by the square root of a chi-squared random variable. For n=1, the chi distribution is a ...

y=x(dy)/(dx)+f((dy)/(dx)) (1) or y=px+f(p), (2) where f is a function of one variable and p=dy/dx. The general solution is y=cx+f(c). (3) The singular solution envelopes are ...

The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...

The phrase "convergence in mean" is used in several branches of mathematics to refer to a number of different types of sequential convergence. In functional analysis, ...

Correlation is the degree to which two or more quantities are linearly associated. In a two-dimensional plot, the degree of correlation between the values on the two axes is ...

Let x->y and u->v be two rules of a term rewriting system, and suppose these rules have no variables in common. If they do, rename the variables. If x_1 is a subterm of x (or ...

The cross-correlation of two complex functions f(t) and g(t) of a real variable t, denoted f*g is defined by f*g=f^_(-t)*g(t), (1) where * denotes convolution and f^_(t) is ...

A delay differential equation (also called a differential delay equation or difference-differential equation, although the latter term has a different meaning in the modern ...

A difference-differential equation is a two-variable equation consisting of a coupled ordinary differential equation and recurrence equation. In older literature, the term ...