Question: Show that if X is a continuous random variable, then min a EjX aj EjX mj , wherem is the median of X. Hint:

Show that if X is a continuous random variable, then min a

EjX ¡aj Æ EjX ¡mj , wherem is the median of X.

Hint: Work out the integral expression of EjX ¡aj and notice that it is differentiable.

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