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The demand has a probability distribution whose cumulative distribution function is denoted . The demand for class 2 comes before demand for class 1. The question now is how much demand for class 2 should be accepted so that the optimal mix of passengers is achieved and the highest revenue is obtained.
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
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 .
The probability that n customers are in the queueing system, the average number of customers in the queueing system, the average number of customers in the waiting line, the average time spent by a customer in the total queuing system, the average time spent by a customer in the waiting line, and finally the probability that the server is busy ...
The store must either be prepared to host an average of 10 occupants or must reduce the time each customer spends in the store to 0.25 hour. The store might achieve the latter by ringing up the bill faster or by adding more counters. We can apply Little's Law to systems within the store. For example, consider the counter and its queue.
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 of Veblen goods are mostly luxurious items such as diamond, gold, precious stones, world-famous paintings, antiques etc. [6] Veblen goods appear to go against the law of demand because of their exclusivity appeal, in the sense that if a price of a luxurious and expensive product is increased, it may attract the status-conscious group ...
For example, the result of a significance test depends on the p-value, the probability of a result as extreme or more extreme than the observation, and that probability may depend on the design of the experiment. To the extent that the likelihood principle is accepted, such methods are therefore denied.