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Probability and queuing theory?
I will rephrase your question, as to "What relationship does queueing theory and probability therory?" Queueing theory is the mathematical study of waiting lines See: http://en.wikipedia.org/wiki/Queueing_theory Wait times, by their nature, are uncertain but can be represented by probability distributions. From a distribution, I may be able to tell that the chance of waiting more than 5 minutes for service is 10%, or that there is a 95% chance that my complete time in a facility (service time and wait time) is less than 15 minutes. On the other side, queueing theory may determine how often those responsible for service have no customers. The theory has broad applications, ranging from computer networks, telephony systems, delivery of goods and services (such as mail, home repair, etc) to an area and customer service in any location where people might stand in line. Traffic analysis uses queueing theory extensively. The "forward" analyses begins with an assumed probability distribution. Given probability distributions that are thought to describe certain activities (number of customers arriving in a particular time span, time spent with each customer and special events -frequency of events and time spent on special events), the distribution of waiting times can be determined mathematically. Thus, probability theory provides the basis (distribution and mathematical theory) for queueing applications. Today, more complex queueing problems are solved by Monte-Carlo simulation, which after thousands (or hundreds of thousands) of repeated runs, can provide nearly the same accuracy of statistics and distributions as those generated from purely mathematical solution. More broadly, queueing modeling and theoretical solutions are within stochastic process analysis.
2 examples how the theory of probability is applied in real life situations?
how theory of probability used in real life
What are the answers to Probability Theory Worksheet 2?
The answer is: WORK THEM OUT
Who discovered probability?
Blaise Pascal and Pierre de Fermat started corresponding over an issue on mathematics of gambling, from which the theory of probability developed in 1654.
What is the relationship between statistical inference and probability theory and how do I support it with examples?
Probability theory is the field of mathematics that enables statistical inferences to be made. All equations used in statistical inferences must be based on mathematics (theorems and proofs) of probability theory. An example to illustrate this. Given a normal probability curve with a mean = 0 and variance of 1, 68% of the area under the curve is in the range of -1 to 1, as calculated from probability theory. Since it is proved by mathematics, we can state it as a fact. If we collect data, and the average of the data is zero, and the standard deviation is 1, then we can infer that we are 68% certain that the population mean lies between -1 to 1. Our conclusion is inferred based on our limited and imperfect sample and the assumption that our population is normally distributed.
