Exercise · ZW-EXPONENTIAL-DISTRIBUTION-005 · ★☆☆ Basic

The mean time between failures of a machine is 5 hours and is exponential. What is \(\lambda\)?

Choose one option.

Show answer

B. \(\tfrac15\)

Explanation

Since \(E[X]=1/\lambda=5\), we get \(\lambda=1/5\) failures per hour.

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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-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?