Exercise · ZW-EXPONENTIAL-DISTRIBUTION-009 · ★★★ Advanced
If \(X\) is exponential with \(\lambda=2\), what is its median?
Choose one option.
Show answer
- D. \(\tfrac{\ln 2}{2}\)
Explanation
Solve \(1-e^{-2m}=\tfrac12\), giving \(m=\ln 2/2\approx0.35\), smaller than the mean \(1/2\).
Review the concept: Exponential distribution
An exponential variable measures the waiting time until the first event of a memoryless process that occurs at a constant rate \(\lambda\); \(f\) is its density.
\[f(x)=\lambda e^{-\lambda x},\quad x\ge0\]
More practice problems: exponential distribution
- ZW-EXPONENTIAL-DISTRIBUTION-001 If X is exponential with λ=2, find E[X].
- ZW-EXPONENTIAL-DISTRIBUTION-002 If X is exponential with λ=3, find Var(X).
- ZW-EXPONENTIAL-DISTRIBUTION-003 If X is exponential with λ=1, find P(X>2).
- ZW-EXPONENTIAL-DISTRIBUTION-004 If X is exponential with λ=2, find P(X≤ 1).
- ZW-EXPONENTIAL-DISTRIBUTION-005 The mean time between failures of a machine is 5 hours and is exponential. What is λ?
- ZW-EXPONENTIAL-DISTRIBUTION-006 If X is exponential with mean 3, find P(X>6).
- ZW-EXPONENTIAL-DISTRIBUTION-007 If X is exponential with λ=1, find P(X>3| X>1).
- ZW-EXPONENTIAL-DISTRIBUTION-008 If X is exponential with λ=2, find P(1<X<2).
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