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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.

Not surprisingly the mean is at the midpoint of the range. Example 2. Let Xhave range [0;2] and density 3. x. 2. Find E(X). 8. answer: E(X) = Z. 2 0. xf(x)dx= Z. 2 0. 3 8 x. 3. dx= 3x. 4. 32 2 = 3 2: Does it make sense that this Xhas mean is in the right half of its range? answer: Yes. Since the probability density increases as xincreases over ...

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