Exercise · ZW-EXPONENTIAL-DISTRIBUTION-001 · ★☆☆ Basic
If \(X\) is exponential with \(\lambda=2\), find \(E[X]\).
Choose one option.
Show answer
- C. \(\tfrac12\)
Explanation
The expectation is \(1/\lambda=1/2\). Confusing it with \(\lambda\) is the most common mistake.
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-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).
- ZW-EXPONENTIAL-DISTRIBUTION-009 If X is exponential with λ=2, what is its median?