PMF Hypergeometric Distribution

Question 1

When does the Hypergeometric distribution apply instead of the Binomial?

Accepted Answer

When sampling is done without replacement from a finite population

Answer

When sampling is done with replacement

Answer

When events are independent

Answer

When the population is infinite

Question 2

A box has 5 red and 7 blue balls. You draw 4 without replacement. What distribution models the number of red balls drawn?

Accepted Answer

Hypergeometric

Answer

Binomial

Answer

Poisson

Answer

Geometric

Question 3

What are the parameters of the Hypergeometric distribution?

Accepted Answer

N (population size), K (successes in population), n (sample size)

Answer

n (trials), p (success probability)

Answer

λ (rate), k (count)

Answer

N (population), p (proportion), n (sample)

Question 4

What is the PMF of the Hypergeometric distribution?

Accepted Answer

P(X=k) = C(K,k)×C(N-K,n-k) / C(N,n)

Answer

P(X=k) = C(n,k) × p^k × (1-p)^(n-k)

Answer

P(X=k) = e^-λ × λ^k / k!

Answer

P(X=k) = (1-p)^(k-1) × p

Question 5

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

Accepted Answer

n × K/N

Answer

K/N

Answer

n × p

Answer

nK

Question 6

When does the Hypergeometric distribution closely approximate the Binomial?

Accepted Answer

When the sample size n is much smaller than the population N

Answer

When n equals N

Answer

When K is very small

Answer

When p is close to 0.5