The Poisson distribution

Introdução à estatística

George Boorman

Curriculum Manager, DataCamp

Poisson processes

  • Average # of events in a period is known
    • but the time or space between events is random
  • Poisson processes
    • Number of animals adopted from an animal shelter per week
    • Number of people arriving at a restaurant per hour
    • Number of website visits in a day

  restaurant.png

1 Image credit: https://unsplash.com/@rodlong
Introdução à estatística

Poisson distribution

  • Probability of some # of events occurring over a fixed period of time
  • Examples
    • Probability of at least five animals adopted from an animal shelter per week
    • Probability of 12 people arriving at a restaurant per hour
    • Probability of less than 200 visits to a website in a day
Introdução à estatística

Lambda ($\lambda$)

  • $\lambda$ = average number of events per time interval
    • Average number of patrons per hour = 20
    • $\lambda$ = the expected value of the distribution!

Poisson distribution with lambda = 20.png

Introdução à estatística

Lambda is the distribution's peak

Three Poisson distributions for restaurant patrons per hour: one with lambda = 10, one with lambda = 20, and one with lambda = 50.png

Introdução à estatística

Central limit theorem still applies!

poisson_distributions_with_100_and_10000_samples_and_lamba_equals_20.png

Introdução à estatística

Probability of 13 patrons in an hour

poisson_distribution_with_lambda_20_and_probability_of_13_equal_to_two_point_seven_one_percent.png

Introdução à estatística

Probability of 25 or more patrons

poisson_distribution_with_lambda_equals_20_and_probability_of_at_last_25_equal_to_elevent_point_two_one_percent.png

Introdução à estatística

Let's practice!

Introdução à estatística

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