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Hypothesis Testing: The Classical Approach (Test Of One Mean)

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CHAPTER 4 Basic Probability and Discrete Probability Distributions

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Discrete Finite Probability Probability 1

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... Note that here we say Borel measure, not Borel probability measure. We have previously discussed the Borel probability measure, which for a finite interval sample space Ω = [u,v] is the unique probability measure on the Borel σ-algebra for Ω such that P((a,b)) = (b-a)/(v-u) for all a,b such that u≤a ...
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... This formula can be expanded. If A, B, C, …, G are independent events, then P(A and B and C and ... and G)  P(A)  P( B)  P(C) P(G)  Example: Suppose the event A is “Allen gets a cold this winter,” B is “Bob gets a cold this winter,” and C is “Chris gets a cold this winter.” P(A) = 0.15, P(B) = ...
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History of statistics

The History of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of the word statistics. In early times, the meaning was restricted to information about states. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, ""statistics"" means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference.Statistical activities are often associated with models expressed using probabilities, and require probability theory for them to be put on a firm theoretical basis: see History of probability.A number of statistical concepts have had an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.
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