Exercise · ZW-POISSON-DISTRIBUTION-002 · ★☆☆ Basic
If \(X\) is Poisson with \(\lambda=3\), compute \(P(X=1)\).
Choose one option.
Show answer
- A. \(3e^{-3}\)
Explanation
With \(k=1\): \(P=e^{-3}\cdot3^1/1!=3e^{-3}\). The exponent of \(e\) is negative.
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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