PMF Hypergeometric Distribution 3

Question 1

For a Hypergeometric distribution, what is the support of X (the number of successes)?

Accepted Answer

max(0, n+K-N) ≤ X ≤ min(n, K)

Answer

0 ≤ X ≤ n

Answer

0 ≤ X ≤ K

Answer

0 ≤ X ≤ N

Question 2

A hypergeometric scenario has N=10, K=6, n=4. What is the maximum possible value of X?

Accepted Answer

4

Answer

6

Answer

10

Answer

3

Question 3

How does the Hypergeometric distribution compare to the Binomial in terms of variance?

Accepted Answer

Hypergeometric has smaller variance due to the finite population correction

Answer

They have identical variance

Answer

Hypergeometric always has larger variance

Answer

Binomial always has smaller variance

Question 4

In a committee of 10 (6 men, 4 women), 3 are randomly selected. What distribution models the number of women selected?

Accepted Answer

Hypergeometric (N=10, K=4, n=3)

Answer

Binomial (n=3, p=0.4)

Answer

Poisson (λ=1.2)

Answer

Negative Binomial

Question 5

For the committee example (N=10, K=4, n=3), what is P(X=2)?

Accepted Answer

C(4,2)×C(6,1)/C(10,3) = 36/120 = 0.3

Answer

C(4,2)/C(10,3) = 6/120 = 0.05

Answer

C(3,2)×(0.4)²×(0.6) ≈ 0.288

Answer

0.4²×0.6 = 0.096

Question 6

Why can't the Binomial distribution be used when sampling is done without replacement from a small population?

Accepted Answer

Draws are no longer independent, violating the Binomial's independence assumption

Answer

The success probability exceeds 1

Answer

The Binomial requires continuous data

Answer

The sample size must equal the population size