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Part CCSIR NET December 2025a-series-systems-failure-probability-is-1-minus-the-fourth-power-of-survival-not-the-fourth-power-itself

A series systems failure probability is 1 minus the fourth power of survival not the fourth power itself

Consider a series system comprising four components, having independent and identically distributed lifetimes with hazard rate λ(t)=1/(1+t),t>0\lambda(t)=1/(1+t), t>0, and survival function S(t), t>0. If Y denotes the lifetime of the series system, then which of the following statements are true?

  1. A.Cumulative hazard function of each component is H(t)=2ln(1+t), t>0
  2. B.S(t)=1/(1+t)2,t>0S(t)=1/(1+t)^{2}, t>0
  3. C.P(Y<1/2)={S(1/2)}4^{4}
  4. D.P(Y<1/2)=65/81✓

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.

See pricing

50 are analysed free — try those first.

Related counterexample: The maximum of independent exponentials is exponential

More on this topic

The chapter behind this: The standard distributions — free to read

From Probability › Standard discrete and continuous distributions

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