Question: Let X be a random variable with c.d.f. F. Suppose that a < b are numbers such that both a and b are medians of

Let X be a random variable with c.d.f. F. Suppose that a < b are numbers such that both a and b are medians of X.
a. Prove that F(a) = 1/2.
b. Prove that there exist a smallest c ≤ a and a largest d ≥ b such that every number in the closed interval [c, d] is a median of X.
c. If X has a discrete distribution, prove that F(d) > 1/2.

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a Since a is assumed to be a median Fa PrX a 12 Since b a is assumed to be a median PrX b 12 If PrX ... View full answer

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