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

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.

De nition: Let X be a continuous random variable with range [a;b] and probability density function f(x). The expected value of Xis de ned by E(X) = Z b xf(x)dx: a Let’s see how this compares with the formula for a discrete random variable: n E(X) = X x ip(x i): i=1 The discrete formula says to take a weighted sum of the values x iof X, where ...

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  Standards, Discrete, Variance, Continuous, Expectations, Deviation, A continuous, Variance and standard deviation

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