2.6.1 Hypergeometric

Question 1

what type of trails would we use the hypergeometric distribution?

Answer 1

dependent trails i.e. when there’s sampling without replacement

Question 2

what does the hypergeometric distribution try to measure?

Answer 2

the probability of x “success” out of n dependent trails from a finite population

Question 3

what is the hypergeometric pmf?

Answer 3

P(X=x) = (c(m, x) * c(N-m, n-x))/c(N, n)

where:
we choose x “successes” out of the m total “successes” in the population, and we choose n-x “failures out of the N-m total “failures” in the population. A sample size of n is drawn from a population of N.

Question 4

what are some key concepts of the pmf?

Answer 4

m + (N - m) = N
x + (n - x) = n
m greater than or equal to n
N -m greater than or equal to n - x
N - m greater than or equal n - x
N greater than or equal to n

Question 5

what are E(X) and Var(X) of a hypergeometric distribution?

Answer 5

E(X) = n* m/N
Var(X) = n * m/N * (N-m)/N * (N-n)/(N-1)

Question 6

can we have more than 2 terms in the numerator of the pmf?

Answer 6

Yes. The standard PMF covers the case where we choose items from two categories, the “success’’ category and the “failure’’ category. However, this can be extended to cover the case where we choose items from more than 2 categories, just by adding terms to the numerator.