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Correlation and regression
The word correlation is used in everyday life to denote some form of association. We…
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Discrete and Continuous Random Variables
A variable is a quantity whose value changes. A discrete variable is a variable whose value is obtained by…
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Bayes’ Theorem
Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently…
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Conditional Probability
The conditional probability of an event B is the probability that the event will occur given the knowledge that…
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Axioms of probability
Chance is a slippery concept. We all know that some random events are more likely…
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Half Range Fourier Series
If a function is defined over half the range, say , instead of the full range…
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Fourier series
A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines.…
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Line Integral
Line integrals (also referred to as path or curvilinear integrals) extend the concept of simple integrals (used to find areas of flat,…
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Cauchy- Riemann equations
Let (1) where (2) so (3) The total derivative of with respect to is then (4)(5) In…