Exercise · ZW-POISSON-DISTRIBUTION-007 · ★★☆ Intermediate
Which of these quantities is best modeled by a Poisson variable?
Choose one option.
Show answer
- C. El número de correos que llegan a un buzón cada hora, a ritmo medio estable
Explanation
Poisson counts independent events per interval at a constant average rate. Waiting time is continuous, a single toss is Bernoulli and “until the first success” is geometric.
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-008 To approximate a binomial with n=200 and p=0.01 by a Poisson, which value of λ is appropriate?
- ZW-POISSON-DISTRIBUTION-009 A Poisson variable satisfies P(X=1)=P(X=2) with λ>0. What is λ?