Joint Distribution
- Provides probabilities for every possible combination of values of two or more random variables.
- Reveals how outcomes of those variables relate to each other (e.g., dependence or association).
- Used to assess the likelihoods of combined outcomes in data involving multiple variables.
Definition
Section titled “Definition”Joint distribution refers to the probability distribution of two or more random variables. It describes the likelihood of each possible combination of values for the random variables.
Explanation
Section titled “Explanation”A joint distribution assigns probabilities to combinations of values taken by the involved random variables, rather than to a single variable at a time. This representation captures how the variables co-occur and thus provides information about their relationship. For example, a joint distribution can indicate that the probability of a particular value of one variable is related to the probability of a particular value of another variable. In applied settings, joint distributions help characterize patterns and associations across variables in a dataset.
Examples
Section titled “Examples”Coin flips
Section titled “Coin flips”One example of a joint distribution is the probability distribution of the number of heads and tails in a series of coin flips. In this example, the two random variables are the number of heads and the number of tails. The joint distribution would describe the probability of each possible combination of the number of heads and tails, such as a distribution where there is a 50% probability of getting two heads and zero tails, or a 25% probability of getting one head and one tail.
Heights and weights
Section titled “Heights and weights”Another example of a joint distribution is the probability distribution of the heights and weights of a group of people. In this example, the two random variables are the height and weight of each person in the group. The joint distribution would describe the probability of each possible combination of height and weight, such as a distribution where there is a high probability of finding people who are both short and light, or a low probability of finding people who are both tall and heavy.
Use cases
Section titled “Use cases”- Understanding the relationship between multiple random variables.
- Assessing the likelihood of different combinations of variable values.
- Researchers and analysts can use joint distributions to gain insights into underlying patterns and trends in complex data sets.
Related terms
Section titled “Related terms”- Random variable
- Probability distribution