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A p-box (probability box). A probability box (or p-box) is a characterization of uncertain numbers consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed.
Bertrand's box paradox: the three equally probable outcomes after the first gold coin draw. The probability of drawing another gold coin from the same box is 0 in (a), and 1 in (b) and (c). Thus, the overall probability of drawing a gold coin in the second draw is 0 / 3 + 1 / 3 + 1 / 3 = 2 / 3 .
The earliest of several probability puzzles related to the Monty Hall problem is Bertrand's box paradox, posed by Joseph Bertrand in 1889 in his Calcul des probabilités. [65] In this puzzle, there are three boxes: a box containing two gold coins, a box with two silver coins, and a box with one of each.
The potential energy in this model is given as = {, < < +,,, where L is the length of the box, x c is the location of the center of the box and x is the position of the particle within the box. Simple cases include the centered box ( x c = 0) and the shifted box ( x c = L /2) (pictured).
The probability that an uncertain number represented by a p-box D is less than zero is the interval Pr(D < 0) = [F(0), F̅(0)], where F̅(0) is the left bound of the probability box D and F(0) is its right bound, both evaluated at zero. Two uncertain numbers represented by probability boxes may then be compared for numerical magnitude with the ...
Box A is transparent and always contains a visible $1,000. Box B is opaque, and its content has already been set by the predictor: If the predictor has predicted that the player will take both boxes A and B, then box B contains nothing. If the predictor has predicted that the player will take only box B, then box B contains $1,000,000.
ODE models of chemical reactor dynamics [5] [6] Pharmacokinetic variability of inhaled VOCs [7] Groundwater modeling [8] Bounding failure probability for series systems [9] Heavy metal contamination in soil at an ironworks brownfield [10] [11] Uncertainty propagation for salinity risk models [12] Power supply system safety assessment [13]
The Ljung–Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the "overall" randomness based on a number of lags, and is therefore a portmanteau test .