Question: A discrete random variable X is called symmetric if for some a and all k, the p.m.f. satisfies pX(a k) = pX(a + k). Suppose

A discrete random variable X is called symmetric if for some a and all k, the p.m.f. satisfies pX(a k) = pX(a + k). Suppose that the mean of X exists. Show that the mean (expected value) is also a median for symmeric random variables, and find a non-symmetric random variable for which the mean is also a median.

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