[機統] Expectations
Let X be a random variable of the continuous type that has pdf f(x).
If m is the unique median of the distribution of X and b is a real constant,
show that E(|X-b|)=E(|X-m|)+2integral(m to b)(b-m)f(x)dx,
provided that the expectations exist.
For what value of b is E(|X-b|) a minimum?
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