Hypergeometric Distribution
Overview
- The Hypergeometric distribution models the probability of drawing a specific number of successes (items of interest) from a finite population without replacement.
- It is commonly used in situations where you have a finite population and want to calculate the probability of drawing a certain number of items of interest in a sample without replacement.
Use Case
- Used in various fields such as quality control (sampling from a production batch), biology (sampling from a population of organisms), and genetics (calculating probabilities of inheritance).
- Probability Mass Function (PMF):
- ( K ): Total number of items of interest in the population
- ( N ): Total population size
- ( n ): Sample size
- ( k ): Number of items of interest in the sample
Example
- Quality Control:
- Suppose a production batch contains 20 defective items out of 100.
- We randomly sample 5 items from the batch without replacement.
- We want to find the probability of obtaining exactly 2 defective items in the sample.
- Using the Hypergeometric PMF:
