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A key example of an optimal stopping problem is the secretary problem. Optimal stopping problems can often be written in the form of a Bellman equation , and are therefore often solved using dynamic programming .
If the capacity left is less than this limit demand for class 2 is rejected. If a continuous distribution F j ( x ) {\displaystyle F_{j}(x)} is used to model the demand, then y 1 ⋆ {\displaystyle y_{1}^{\star }} can be calculated using what is called Littlewood’s rule :
Graph showing relationships between the rule of twelfths (coloured bars), a sine wave (dashed blue curve) and a clockface, if high tide occurs at 12:00. The rule of twelfths is an approximation to a sine curve. It can be used as a rule of thumb for estimating a changing quantity where both the quantity and the steps are easily divisible by 12 ...
In general, any infinite series is the limit of its partial sums. For example, an analytic function is the limit of its Taylor series, within its radius of convergence. = =. This is known as the harmonic series. [6]
Example of a stopping time: a hitting time of Brownian motion.The process starts at 0 and is stopped as soon as it hits 1. In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time [1]) is a specific type of “random time”: a random variable whose value is interpreted as the time at ...
Examples abound, one of the simplest being that for a double sequence a m,n: it is not necessarily the case that the operations of taking the limits as m → ∞ and as n → ∞ can be freely interchanged. [4] For example take a m,n = 2 m − n. in which taking the limit first with respect to n gives 0, and with respect to m gives ∞.
In practice, a consumer may not always pick an optimal bundle. For example, it may require too much thought or too much time. Bounded rationality is a theory that explains this behaviour. Examples of alternatives to utility maximisation due to bounded rationality are; satisficing, elimination by aspects and the mental accounting heuristic.
The mathematical problem appears to date from 1888 [2] where Edgeworth used the central limit theorem to determine the optimal cash reserves to satisfy random withdrawals from depositors. [3] According to Chen, Cheng, Choi and Wang (2016), the term "newsboy" was first mentioned in an example of the Morse and Kimball (1951)'s book. [4]