Exercise · ZW-POISSON-DISTRIBUTION-006 · ★★☆ Intermediate
If \(X\) is Poisson with \(\lambda=2\), compute \(P(X\ge1)\).
Choose one option.
Show answer
- D. \(1-e^{-2}\)
Explanation
By the complement, \(P(X\ge1)=1-P(X=0)=1-e^{-2}\). The value \(1-2e^{-2}\) also subtracts \(P(X=1)=2e^{-2}\), so it equals \(P(X\ge2)\).
Review the concept: Poisson distribution
A Poisson variable \(X\) counts independent events, at a constant average rate, in a fixed interval; its parameter \(\lambda\) is the mean number of events and \(P(X=k)\) the probability of observing \(k\).
\[P(X=k)=\frac{e^{-\lambda}\lambda^{k}}{k!},\quad k=0,1,2,\dots\]
More practice problems: poisson distribution
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