Mathematics · Probability and Reliability Theory
Let X1, X2, X3 be a random sample from a continuous distribution with cumulative distribution function F(t) and failure rate function r(t) = f(t)1 - F(t) for t > 0, where F(0) = 0. If r(t) = 1 for all t > 0, which of the following statements is true?
- 1P(max{X1, X2} < X3) = 13
- 2P(min{X1, X2} < X3) = 23✓
- 3P(min{X1, X2} > 1) = 12e
- 4P(max{X1, X2} < 1) = 12e
Correct answer
P(min{X1, X2} < X3) = 23
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