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1313_section8o3 - Section 8.3 Variance and Standard...

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Section 8.3 – Variance, Standard Deviation and Chebychev’s Inequality 1 Section 8.3 Variance and Standard Deviation The Variance of a random variable X is the measure of degree of dispersion, or spread, of a probability distribution about its mean (i.e. how much on average each of the values of X deviates from the mean.). Note: A probability distribution with a small (resp., large) spread about its mean will have a small (resp., large) variance. Variance of a Random Variable X Suppose a random variable has the probability distribution x 1 x 2 x n x P(X=x) 1 p 2 p n p and expected value E(X) = μ . Then the variance of the random variable X is 2 2 2 2 2 1 1 ) ( ... ) ( ) ( ) ( μ μ μ - + + - + - = n n x p x p x p X Var Note: We square each since some may be negative. Standard Deviation measures the same thing as the variance. The standard deviation of a random variable X is ) ( X Var = σ Note: As stated above the standard deviation measures the same thing as the variance.
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