Exercise · ZW-POISSON-DISTRIBUTION-001 · ★☆☆ Basic
If \(X\) is Poisson with \(\lambda=2\), compute \(P(X=0)\).
Choose one option.
Show answer
- C. \(e^{-2}\)
Explanation
With \(k=0\): \(P=e^{-2}\cdot2^0/0!=e^{-2}\). The value \(2e^{-2}\) would be \(P(X=1)\).
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 \(k\).
\[P(X=k)=\frac{e^{-\lambda}\lambda^{k}}{k!},\quad k=0,1,2,\dots\]
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