PMF Hypergeometric Distribution 2

Question 1

A lot of 20 items contains 4 defectives. A sample of 5 is drawn without replacement. What is E[X], the expected number of defectives?

Accepted Answer

1

Answer

0.8

Answer

2

Answer

4

Question 2

What is the variance of a Hypergeometric distribution with parameters N, K, n?

Accepted Answer

n × (K/N) × (1 - K/N) × (N-n)/(N-1)

Answer

n × p × (1-p)

Answer

n × (K/N) × (1 - K/N)

Answer

K(N-K)n / N²

Question 3

In quality control, 3 defective and 12 good items are in a batch of 15. Two items are drawn without replacement. What is P(both defective)?

Accepted Answer

Both A and C are correct

Answer

C(3,2)×C(12,0)/C(15,2) = 3/105 ≈ 0.029

Answer

C(3,2)/C(15,2) ≈ 0.057

Answer

(3/15) × (2/14) ≈ 0.029

Question 4

The finite population correction factor in the Hypergeometric variance is (N-n)/(N-1). What happens to this factor as n approaches N?

Accepted Answer

It approaches 0, reducing the variance

Answer

It approaches 1, giving the Binomial variance

Answer

It becomes negative

Answer

It approaches N

Question 5

Which term describes (N-n)/(N-1) in the Hypergeometric variance formula?

Accepted Answer

Finite population correction factor

Answer

Normalizing constant

Answer

Skewness correction

Answer

Continuity correction

Question 6

A card is drawn from a deck of 52 without replacement for 5 draws. Which distribution models the number of aces drawn?

Accepted Answer

Hypergeometric (N=52, K=4, n=5)

Answer

Binomial (n=5, p=4/52)

Answer

Poisson (λ = 5×4/52)

Answer

Geometric (p=4/52)