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.

The discrete formula says to take a weighted sum of the values x iof X, where the weights are the probabilities p(x ... that is often easier to use in hand calculations. The proofs of properties 2 and 3 are essentially identical to those in the discrete case. ... is the value such that there is an area of pto the left of q. p. and an area of 1 ...

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  Area, Standards, Variance, Calculation, Weighted, Expectations, Deviation, Variance and standard deviation

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