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Variance and Higher Moments - Comprehensive Introduction

This page contains the definition of variance and higher moments using the expected value. It contains properties, with proofs, of variance, skew, and kurtosis. It also contains Chebyshev’s inequality. It also has discussions about the variance of special distributions, some of these are given, some the reader is asked to find (answers are given through a small link at the end of the page). It contains links to simulators and directions for the student to use the simulator to observe various properties. Finally, there is a discussion of vector space concepts leading to Minkowski’s inequality, Lyapunov’s inequality, and convergence.
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Kyle Siegrist
Lisa Green
Virtual Laboratories in Probability and Statistics
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