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

The Hypergeometric distribution applies when drawing without replacement from a finite population, making draws dependent.

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

Sampling without replacement from a finite population of two types is modeled by the Hypergeometric distribution.

Question 3

What are the parameters of the Hypergeometric distribution?

Accepted Answer

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

Answer

The Hypergeometric distribution is parameterized by N (total population), K (number of successes in population), and n (sample size).

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

The Hypergeometric PMF uses combinations: C(K,k) ways to choose k successes times C(N-K, n-k) ways to choose remaining items, divided by C(N,n) total ways.

Question 5

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

Accepted Answer

n × K/N

Answer

E[X] = n × K/N, which is the sample size times the population proportion of successes.

PMF - Probability Mass Function Practice Test

PMF - Probability Mass Function Practice Test

PMF Hypergeometric Distribution