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Estimators and Parameters
Estimators and Parameters

... Populations are characterized by numerical measures called parameters. In many statistical applications, we want to use information from a sample to estimate one or more population parameters. An estimator is a rule that tells us how to calculate the value of an estimate based on measurements contai ...
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... In the design of the voice communication system, a model is needed for the number of calls and the duration of calls. Even knowing that on average, calls occur every five minutes and that they last five minutes is not sufficient. If calls arrived precisely at five-minute intervals and lasted for pre ...
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... diagnosis fails for three main reasons. Laziness it is too much work to list an exceptionless rule-set and actually too difficult to use such a rule-set. Theoretical ignorance Medical science has no complete theory for the domain. Practical ignorance Even if we know all the rules, we might be uncert ...
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... EM Summary (so far) EM is a general procedure for learning in the presence of unobserved variables. We have shown how to use it in order to estimate the most likely density function for a mixture of (Bernoulli) distributions. EM is an iterative algorithm that can be shown to converge to a local max ...
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Probability

Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of ""heads"" equals the probability of ""tails"", so the probability is 1/2 (or 50%) chance of either ""heads"" or ""tails"".These concepts have been given an axiomatic mathematical formalization in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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