Part CCSIR NET December 2024hazards-add-only-for-independent-variables

Hazards add only for independent variables

Let $X_{1}$ and $X_{2}$ be random variables having absolutely continuous distribution functions. Let $h_{i} (t)$ denote the hazard function of $X_{i}, i = 1, 2$ . If $h_{1} (t) \leq h_{2} (t)$ for all $t \in R$ , then which of the following statements are true?

A. $P (X_{1} > 1) \geq P (X_{2} > 1)$ ✓
B. $P (X_{1} > 1) \leq P (X_{2} > 1/2)$
C. $E (X_{1}) \geq E (X_{2})$ provided both the expectations exist.✓
D. $h (t) = h_{1} (t) + h_{2} (t), t \in R$ , is the hazard function of the random variable Y = min{ $X_{1}, X_{2}$ }.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Hazards add only for independent variables

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