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Summation Notation
Summation Notation

... If we take all possible samples of N = 100 from a given population, the resulting distribution of the sample means have X =  The distribution would be normally distributed with a standard deviation known as standard error of mean (or simply the standard error). The standard error is symbolized as S ...
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... Joe takes a test in Biology and Math.  Each test has data values that are normally distributed.  He  scores an 85% on his Biology test and an 80% on his Math test.  The mean grade for the Biology test  is 88% with a standard deviation of 3.  The mean grade for the Math test is 78% with a standard  d ...
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AMS 7L is required for AMS 7, There are about 10 of you

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docx - David Michael Burrow

... At the beginning of the semester a teacher tells her students they are part of a special study and will be learning by a special new method. Then the teacher proceeds to make no changes and teaches exactly the same way she always has. Even so, at the end of the semester, the students show significan ...
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Time series



A time series is a sequence of data points, typically consisting of successive measurements made over a time interval. Examples of time series are ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. Time series are very frequently plotted via line charts. Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, intelligent transport and trajectory forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements.Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. While regression analysis is often employed in such a way as to test theories that the current values of one or more independent time series affect the current value of another time series, this type of analysis of time series is not called ""time series analysis"", which focuses on comparing values of a single time series or multiple dependent time series at different points in time.Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility.)Time series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language.).
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