PMF Poisson Distribution 2

Question 1

The Poisson distribution is often used as an approximation for which distribution when n is large and p is small?

Accepted Answer

Binomial distribution

Answer

Geometric distribution

Answer

Hypergeometric distribution

Answer

Uniform distribution

Question 2

For a Poisson PMF, which of the following is true about its support (possible values)?

Accepted Answer

X can take any non-negative integer value (0, 1, 2, …)

Answer

X can only take values between 0 and 1

Answer

X can take any positive real value

Answer

X is limited to values from 0 to λ

Question 3

If X ~ Poisson(λ=4), what is P(X=1)?

Accepted Answer

4e^-4 ≈ 0.073

Answer

e^-4 ≈ 0.018

Answer

8e^-4 ≈ 0.147

Answer

4e^4

Question 4

What is the sum of all probabilities P(X=k) for k=0,1,2,… in a Poisson distribution?

Accepted Answer

1

Answer

λ

Answer

e^λ

Answer

e^-λ

Question 5

Two independent Poisson random variables X ~ Poisson(λ₁) and Y ~ Poisson(λ₂) are added. What is the distribution of X + Y?

Accepted Answer

Poisson(λ₁ + λ₂)

Answer

Poisson(λ₁ × λ₂)

Answer

Poisson(λ₁ - λ₂)

Answer

Normal(λ₁ + λ₂, λ₁ + λ₂)

Question 6

In the Poisson PMF, what role does the constant e (Euler's number ≈ 2.718) play?

Accepted Answer

It is part of the normalizing factor ensuring probabilities sum to 1

Answer

It represents the average number of events

Answer

It scales the number of trials

Answer

It defines the upper bound of the distribution