Poisson distribution

What is the Poisson distribution?

A probability distribution that represents the number of events occurring within a fixed interval of time or space.

When is the Poisson distribution used?

When events occur independently and the average number of events in the interval is known.

What is the formula for the Poisson probability mass function?

P(X=k) = (λ^k * e^(-λ)) / k! where λ is the average rate and k is the number of occurrences.

What does the parameter 'λ' represent in Poisson distribution?

The average number of occurrences in the interval.

What are some real-world examples of Poisson distribution?

Modeling the number of phone calls received by a call center per hour or the number of decay events from a radioactive source.

What characteristic distinguishes the Poisson distribution from the binomial distribution?

The Poisson distribution is used for rare events, while the binomial distribution is for a fixed number of trials.

What is the mean and variance of a Poisson distribution?

Both the mean and variance are equal to λ.

What is the cumulative distribution function (CDF) in Poisson distribution?

It provides the probability that a random variable X is less than or equal to a certain value k.

What assumption is made about events in a Poisson distribution?

Events are independent; the occurrence of one event does not affect the probability of another.

How do you calculate Poisson probabilities for multiple k values?

Use the Poisson formula for each k and sum the probabilities for intervals of interest.