Part CCSIR NET December 2023min-of-exponentials

Min of exponentials

Let $X_{i} (i = 1, 2)$ be independent with densities $f_{i} (x) = i$ $e^{- i x}$ for x ≥ 0. Consider a series system of two independent components with lifetimes $X_{1}$ and $X_{2}$ , and let X denote the lifetime of the system. Which of the following statements are true?

A.P(X > 4) = P(X > 1)P(X > 2)
B.P(X > 4 | X > 2) = P(X > 2)✓
C.E(X) = 1/3✓
D.6X ~ $χ_{3}^{2}$

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, and why this one tests dependence misread.

See pricing

50 are analysed free — try those first.

The trap it tests

Dependence misread

Independence, pairwise vs mutual, or correlation vs dependence.

Drill statements like this

The chapter behind this: Joint distributions, transformations and order statistics — free to read

From Probability › Joint distributions, transformations, order statistics

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