PMF Poisson Distribution

Question 1

Which formula correctly expresses the Poisson PMF for k occurrences with rate λ?

Accepted Answer

P(X=k) = (e^-λ × λ^k) / k!

Answer

The Poisson PMF is P(X=k) = (e^-λ × λ^k) / k! where λ is the average rate and k is a non-negative integer.

Question 2

In a Poisson distribution with λ = 3, what is the mean of the distribution?

Accepted Answer

3

Answer

For a Poisson distribution, both the mean and variance equal λ, so the mean is 3.

Question 3

A call center receives an average of 5 calls per hour. What distribution models the number of calls in any given hour?

Accepted Answer

Poisson distribution

Answer

The Poisson distribution models counts of events occurring at a constant average rate over a fixed interval.

Question 4

What is the variance of a Poisson distribution with λ = 7?

Accepted Answer

7

Answer

For a Poisson distribution, the variance equals λ, so Var(X) = 7.

Question 5

Which condition must be met for the Poisson distribution to be a valid model?

Accepted Answer

Events must occur independently at a constant average rate

Answer

The Poisson model requires events to be independent and to occur at a constant average rate within a fixed interval.

PMF - Probability Mass Function Practice Test