Exercise · ZW-POISSON-DISTRIBUTION-010 · ★★★ Advanced
\(X\) and \(Y\) are independent Poisson variables with parameters 2 and 3. What is the probability that \(X+Y=0\)?
Choose one option.
Show answer
- B. \(e^{-5}\)
Explanation
The sum of independent Poisson variables is Poisson with parameter \(2+3=5\), so \(P(X+Y=0)=e^{-5}\). It matches \(e^{-2}e^{-3}\), the probability that both are 0.
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
- ZW-POISSON-DISTRIBUTION-001 If X is Poisson with λ=2, compute P(X=0).
- ZW-POISSON-DISTRIBUTION-002 If X is Poisson with λ=3, compute P(X=1).
- ZW-POISSON-DISTRIBUTION-003 If X is Poisson with λ=4.5, compute E[X].
- ZW-POISSON-DISTRIBUTION-004 If X is Poisson with λ=5, compute Var(X).
- ZW-POISSON-DISTRIBUTION-005 A switchboard receives on average 6 calls per hour, with independent arrivals at a constant rate. W…
- ZW-POISSON-DISTRIBUTION-006 If X is Poisson with λ=2, compute P(X≥1).
- ZW-POISSON-DISTRIBUTION-007 Which of these quantities is best modeled by a Poisson variable?
- ZW-POISSON-DISTRIBUTION-008 To approximate a binomial with n=200 and p=0.01 by a Poisson, which value of λ is appropriate?