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Q5Section A (Section A)5 of 60

Upper bound for the third quartile

Let YY be a continuous random variable such that P(Y>0)=1P(Y>0)=1 and E(Y)=1E(Y)=1. For p∈(0,1)p\in(0,1), let ξp\xi_p denote the pthp^{\mathrm{th}} quantile of the probability distribution of the random variable YY. Then which of the following statements is always correct?

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