What is Poisson distribution?

The probability distribution of the number of times a rare event that occurs independently happens within a fixed time or area. With mean λ, the probability of k occurrences is λᵏ × e^(−λ) ÷ k!, and both the mean and the variance are λ. It is used to model the number of requests arriving at a server, the number of inquiries to a service desk, the number of defects on a wafer and the number of photons. The probability of zero defects, e^(−λ), corresponds to the Poisson yield model. When the number of arrivals follows a Poisson distribution, the intervals between arrivals follow an exponential distribution.

Japanese name: ポアソン分布

Poisson distribution appears in 1 practice question across 1 topic, including Probability, Statistics and Queueing.

Field: Probability, Statistics and Queueing

Try it: questions about Poisson distribution

Inquiries to a service desk arrive at random, independently of one another, at an average of 3 per hour, and the number arriving in one hour follows a Poisson distribution. Taking e⁻³ ≈ 0.0498, which of the following is closest to the probability that exactly 2 arrive in a given hour?

A0.050
B0.149
C0.224

Show answer and explanation

Answer: C. 0.224

For a Poisson distribution with mean λ, the probability of k events is P(k) = λᵏ × e^(−λ) ÷ k!. With λ = 3 and k = 2, P(2) = 3² × e⁻³ ÷ 2 = 4.5 × 0.0498 ≈ 0.224. The Poisson distribution describes how many times a rare event occurs in a fixed time or area, and it is also used for the number of defects on a wafer.

Poisson distribution in the explanations

For a Poisson distribution with mean λ, the probability of k events is P(k) = λᵏ × e^(−λ) ÷ k!.
Inquiries to a service desk arrive at random, independently…

Questions that mention Poisson distribution (1)

Inquiries to a service desk arrive at random, independently of one another, at an average of 3 per hour, and the number arriving in one hour follows a Poisson distribution. Taking e⁻³ ≈ 0.0498, which of the following is closest to the probability that exactly 2 arrive in a given hour?

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