17. Let X be a continuous random variable with probability density function

f. A number t is said to be the median of X if

By Exercise 9, Section 6.1, X is symmetric about α if and only if for all x we have f(α − x) = f(α + x). Show that if X is symmetric about α, then E(X) = Median(X) = α.

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P(X t) = P(X t) =