Explanation Assume a continuous random variable X has the probability density function f ( x ) on [ a , b ] . The expected value E ( X ) is μ . Therefore, the variance Var ( X ) of the continuous random variable X is written below. Var ( X ) = ∫ a b ( x − μ ) 2 f ( x ) d x Therefore, the variance Var ( X ) of a continuous random variable X is ∫ a b ( x − μ ) 2 f ( x ) d x

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Chapter 10.2, Problem 3CQ

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The variance and standard deviation of a continuous random variable X.

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