The most important special case is e j 1 m x j j 1 m

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The most important special case is E j 1 m X j j 1 m E X j 47
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Unlike the mean, the median is not a linear operator. In fact, in general Med X Y Med X Med Y . As a simple example, let X take on the values 1,0 with probabilities 1/3,2/3 and Y take on the values 0,1 with probabilities 1/3,2/3 and assume they are independent. The random variable Z X Y takes on the values 1,0,1 with probabilities 1/9,4/9,4/9 . So Med X Y Med Z 0 Med X Med Y 0 1 1. 48
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