Joint distribution and joint density are both ways of representing the relationship between two or more random variables in statistics. The main difference is that joint distribution refers to the probability of specific values occurring for each of the variables, while joint density refers to the probability density of these values. In other words, joint distribution is discrete and joint density is continuous.
Joint distribution is calculated by multiplying the individual probabilities of each variable, while joint density is calculated by taking the partial derivatives of the joint probability distribution function with respect to each variable.
No, joint distribution and joint density are not interchangeable terms. While they both describe the relationship between random variables, they represent different concepts and are calculated differently.
Joint distribution is commonly used in discrete data analysis, such as in the analysis of categorical data or counts. It is also used in hypothesis testing and probability calculations.
Joint density is typically used in continuous data analysis, such as in the analysis of measurements or continuous variables. It is also used in probability calculations and for finding the expected value or mean of a continuous random variable.