Mathematics · Probability Theory
Let X 1 and X 2 be independent lifetimes of two components, each following an exponential distribution with probability density function f(x) = 1 2 e -x/2 for x > 0, and 0 otherwise. Let Y 1 = X 1 + X 2 , Y 2 = max{X 1 , X 2 }, and Y 3 = min{X 1 , X 2 }. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Var(Y 1 + Y 2 + Y 3 ) = 32
- 2P(Y 3 > 2) = e -2✓
- 3P(Y 2 > 2) = e -2
- 4P(Y 1 > 2) = 2e -1
Correct answer
P(Y 3 > 2) = e -2
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