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

P(X=k) = (λ^k × k!) / e^λ

Answer

P(X=k) = (e^λ × k^λ) / k!

Answer

P(X=k) = λ^k / (e^λ × k)

Question 2

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

Accepted Answer

3

Answer

9

Answer

1.73

Answer

6

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

Normal distribution

Answer

Binomial distribution

Answer

Uniform distribution

Question 4

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

Accepted Answer

7

Answer

49

Answer

2.65

Answer

14

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 number of trials must be fixed

Answer

Each trial must have exactly two outcomes

Answer

The probability of success must exceed 0.5

Question 6

If X ~ Poisson(λ=2), what is P(X=0)?

Accepted Answer

e^-2 ≈ 0.135

Answer

0.5

Answer

2e^-2 ≈ 0.271

Answer

1 - e^-2 ≈ 0.865