Reading 6a: Expectation, Variance and Standard Deviation ...

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Expectation, Variance and Standard Deviation forContinuous Random VariablesClass 6, Orloff and Jonathan Bloom1 Learning Goals1. Be able to compute and interpret expectation, Variance , and Standard Deviation forcontinuous random Be able to compute and interpret quantiles for discrete and continuous random IntroductionSo far we have looked at expected value, Standard Deviation , and Variance for discreterandom variables. These summary statistics have the same meaning for continuous randomvariables: The expected value =E(X) is a measure of location or central tendency. The Standard Deviation is a measure of the spread or scale. The Variance 2= Var(X) is the square of the Standard move from discrete to continuous, we will simply replace the sums in the formulas byintegrals.

4 Variance. Now that we’ve de ned expectation for continuous random variables, the de nition of vari-ance is identical to that of discrete random variables. De nition: Let Xbe a continuous random variable with mean . The variance of Xis Var(X) = E((X ) 2): 4.1 Properties of Variance. These are exactly the same as in the discrete case. 1.

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