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The variance of the sum or difference (y = x 2τ − x τ) of two independent samples of a random variable is twice the variance of the random variable (σ y 2 = 2σ x 2). The MDEV is the second difference of independent phase measurements (x) that have a variance (σ x 2).
Five eight-step random walks from a central point. Some paths appear shorter than eight steps where the route has doubled back on itself. (animated version)In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some mathematical space.
An accelerometer measures proper acceleration, which is the acceleration it experiences relative to freefall and is the acceleration felt by people and objects. [2] Put another way, at any point in spacetime the equivalence principle guarantees the existence of a local inertial frame, and an accelerometer measures the acceleration relative to that frame. [4]
English: One million steps in a two-dimensional random walk, at 1500 steps per second. At each step, the particle randomly moves to any one of the eight positions in its Moore neighbourhood. The grid is 400x400 square with toroidal boundary conditions (i.e. going off one edge reappears on the opposite edge).
Therefore, the random walk occurs on the weighted graph (see Doyle and Snell for an introduction to random walks on graphs [2]). Although the initial algorithm was formulated as an interactive method for image segmentation, it has been extended to be a fully automatic algorithm, given a data fidelity term (e.g., an intensity prior). [3]
In science, Brownian noise, also known as Brown noise or red noise, is the type of signal noise produced by Brownian motion, hence its alternative name of random walk noise. The term "Brown noise" does not come from the color , but after Robert Brown , who documented the erratic motion for multiple types of inanimate particles in water.
An unbiased random walk is non-ergodic. Its expectation value is zero at all times, whereas its time average is a random variable with divergent variance. Suppose that we have two coins: one coin is fair and the other has two heads. We choose (at random) one of the coins first, and then perform a sequence of independent tosses of our selected coin.
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