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

The Correct Option is B

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