Exercise · ZW-POISSON-DISTRIBUTION-004 · ★☆☆ Basic
If \(X\) is Poisson with \(\lambda=5\), compute \(\operatorname{Var}(X)\).
Choose one option.
Show answer
- B. \(5\)
Explanation
The Poisson variance equals the mean: \(\operatorname{Var}(X)=\lambda=5\). The value \(\sqrt5\) would be the standard deviation.
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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