Let X1 and X2 be random variables having absolutely continuous distribution functions. Let hi(t) denote the hazard function of Xi, i = 1, 2. If h1(t) ≤ h2(t) for all t ∈ ℝ, then which of the following statements is necessarily true?

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Mathematics · Probability and Statistics

Let X1 and X2 be random variables having absolutely continuous distribution functions. Let hi(t) denote the hazard function of Xi, i = 1, 2. If h1(t) ≤ h2(t) for all t ∈ ℝ, then which of the following statements is necessarily true?

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P(X1 > 1) ≥ P(X2 > 1)

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Answer 1

P(X1 > 1) ≥ P(X2 > 1)

Answer 2

P(X1 > 1) ≤ P(X2 > 0.5)

Answer 3

E(X1) ≤ E(X2) provided both expectations exist

Answer 4

h(t) = h1(t) + h2(t) is always the hazard function of Y = max{X1, X2}

Let X1 and X2 be random variables having absolutely continuous distribution functions. Let hi(t) denote the hazard function of Xi, i = 1, 2. If h1(t) ≤ h2(t) for all t ∈ ℝ, then which of the following statements is necessarily true?

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Let X1 and X2 be random variables having absolutely continuous distribution functions. Let hi(t) denote the hazard function of Xi, i = 1, 2. If h1(t) ≤ h2(t) for all t ∈ ℝ, then which of the following statements is necessarily true?

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