Question: A continuous random variable X is called symmetric about c if its density f satisfies the condition f(c x) = f(c + x) for

A continuous random variable X is called symmetric about c if its density f satisfies the condition f(c − x) = f(c + x) for all x. Show that: (i) If X is symmetric about c and E(X) exists, then E(X) =

c. (ii) If X is symmetric about 0, then all moments of odd order (if they exist) are equal to 0.

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