Poisson distribution in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Poisson distribution used for?

The Poisson distribution models the number of times an event happens in a fixed interval of time or space, when events occur independently and at a constant average rate.

beginner

What parameter does the Poisson distribution use?

It uses a single parameter called lambda (λ), which represents the average number of events in the interval.

intermediate

How do you calculate the probability of exactly k events in Poisson distribution?

The probability is given by P(k) = (λ^k * e^(-λ)) / k!, where k is the number of events, λ is the average rate, and e is Euler's number.

beginner

In Python's scipy library, which function generates Poisson probabilities?

The function is scipy.stats.poisson.pmf(k, mu), where k is the number of events and mu is the average rate λ.

beginner

What real-life example fits the Poisson distribution?

Counting the number of emails you receive in an hour, assuming emails come independently and at a steady average rate.

What does the parameter λ represent in a Poisson distribution?

A The variance of the events

B The average number of events in the interval

C The total number of events observed

D The time between events

λ (lambda) is the average number of events expected in the fixed interval.

Which scipy function calculates the probability mass function for Poisson?

A scipy.stats.poisson.pmf

B scipy.stats.poisson.cdf

C scipy.stats.norm.pdf

D scipy.stats.binom.pmf

pmf stands for probability mass function, which gives the probability of exactly k events.

If λ = 3, what is the probability of 0 events occurring?

A 3^0

B 0

C e^(-3)

D 1

P(0) = (3^0 * e^(-3)) / 0! = e^(-3).

Poisson distribution assumes events occur:

A Only once

B In clusters

C With increasing frequency over time

D Independently and at a constant average rate

Poisson assumes independent events with a steady average rate.

Which of these is NOT a typical use of Poisson distribution?

A Height of people in a group

B Number of cars passing a checkpoint

C Number of decay events from a radioactive source

D Number of phone calls received per hour

Height is continuous and usually modeled by normal distribution, not Poisson.

Explain the Poisson distribution and when it is used.

Think about counting rare events over time or space.

Describe how to calculate the probability of k events using the Poisson formula.

Remember the role of e and factorial in the formula.