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Prove that the quantile function F ?1 of a general rando

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Prove that the quantile function F ?1 of a general random variable X has the following three properties that are analogo

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Prove that the quantile function F ?1 of a general random variable X has the following three properties that are analogous to properties of the c.d.f.: a. F ?1 is a nondecreasing function of p for 0 0 F ?1(p) and x1 = limp?1 p 0, and x1 equals the least upper bound on the set of numbers d such that Pr(X ? d) > 0. c. F ?1 is continuous from the left; that is F ?1(p) = F ?1(p?) for all 0

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