We have seen that the binomial distribution is based on the hypothesis of an infinite population N, a condition that can be practically realized by sampling from a finite population with replacement.
If this does not occur, meaning if we are sampling from a population without replacement, we must use the hypergeometric distribution. (In reality, if N is large, the hypergeometric probability density function tends towards the binomial).
The hypergeometric distribution is used to calculate the probability of obtaining a certain number of successes in a series of binary trials (yes or no), which are dependent and have a variable probability of success.
The hypergeometric distribution allows us to answer questions like:
If I take a sample of size N, in which M elements meet certain requirements, what is the probability of drawing x elements that meet those requirements?
Continue reading “The Hypergeometric Distribution”