PMF Poisson Distribution 1 — Questions and Answers
Question 1: Which formula correctly expresses the Poisson PMF for k occurrences with rate λ?
- P(X=k) = (e^-λ × λ^k) / k! (Correct answer)
- P(X=k) = (λ^k × k!) / e^λ
- P(X=k) = (e^λ × k^λ) / k!
- P(X=k) = λ^k / (e^λ × k)
Correct answer: P(X=k) = (e^-λ × λ^k) / k!
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?
- 3 (Correct answer)
- 9
- 1.73
- 6
Correct answer: 3
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?
- Poisson distribution (Correct answer)
- Normal distribution
- Binomial distribution
- Uniform distribution
Correct answer: Poisson distribution
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?
- 7 (Correct answer)
- 49
- 2.65
- 14
Correct answer: 7
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?
- Events must occur independently at a constant average rate (Correct answer)
- The number of trials must be fixed
- Each trial must have exactly two outcomes
- The probability of success must exceed 0.5
Correct answer: Events must occur independently at a constant average rate
The Poisson model requires events to be independent and to occur at a constant average rate within a fixed interval.
Question 6: If X ~ Poisson(λ=2), what is P(X=0)?
- e^-2 ≈ 0.135 (Correct answer)
- 0.5
- 2e^-2 ≈ 0.271
- 1 - e^-2 ≈ 0.865
Correct answer: e^-2 ≈ 0.135
P(X=0) = (e^-2 × 2^0) / 0! = e^-2 ≈ 0.135.
PMF Poisson Distribution 1
Which formula correctly expresses the Poisson PMF for k occurrences with rate λ?