Let X be a random variable with c.d.f. F. Suppose that a < b are numbers such
Question:
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 the full answer
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Related Book For 
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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