Question

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

• A. $\xi_{0.75} \geq 5$
• B. $\xi_{0.75} \leq 4$
• C. $\xi_{0.25} \geq 4$
• D. $\xi_{0.25} = 2$

Answer 1

Answer: (B)

$\xi_{0.75} \leq 4$

Answer 2

The correct option is (B): $\xi_{0.75} \leq 4$