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

The Poisson distribution approximates the Binomial when n is very large and p is very small, using λ = np.

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

The support of a Poisson random variable is {0, 1, 2, 3, …}, all non-negative integers.

Question 3

If X ~ Poisson(λ=4), what is P(X=1)?

Accepted Answer

4e^-4 ≈ 0.073

Answer

P(X=1) = (e^-4 × 4^1) / 1! = 4e^-4 ≈ 0.073.

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

Like all valid PMFs, the Poisson probabilities sum to 1 over all possible values.

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

The sum of independent Poisson random variables is also Poisson with rate equal to the sum of the individual rates.

PMF - Probability Mass Function Practice Test