Wednesday, August 17, 2011

Basic Concepts: Defining The Mean and Variance

"E[X] is the center of gravity (or centroid) of the unit mass that is determined by the density function of X. So the mean of X is a measure
of where the values of the random variable X are" centered…. The variance of X will be a measure of the spread or dispersion of the density of X
" ---Mood, Alexander McFar1ane, INTRODUCTION TO THE THEORY OF STATISTICS  1963.

“The variance of a distribution provides a measure of the spread or dispersion of the distribution about its mean. A small value of the variance indicates that the probability distribution is tightly concentrated around the mean (μ ); and a large value of the variance typically indicates that the probability distribution has a wide spread about the mean (μ )….the variance of X is the second central moment of X” – DeGroot & Schervish. Probability and Statistics 2002.



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