Statistics - difference between joint distribution and joint density?

In summary, joint distribution and joint density are ways of representing the relationship between random variables in statistics. Joint distribution refers to the probability of specific values occurring, while joint density refers to the probability density. They are calculated differently, with joint distribution being discrete and joint density being continuous. They are not interchangeable terms and are used in different situations, with joint distribution being used for discrete data analysis and joint density being used for continuous data analysis.
  • #1
Kuma
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Homework Statement



This is just a general question about understanding.

What is the difference between a joint distribution functions vs. a joint density function.


Homework Equations





The Attempt at a Solution



Are joint density functions basically the joint distributions of continuous Random variables and joint distribution pertain to discrete random variables?
 
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  • #2

1. What is the difference between joint distribution and joint density in statistics?

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.

2. How are joint distribution and joint density calculated?

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.

3. Can joint distribution and joint density be used interchangeably?

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.

4. When is joint distribution used in statistical analysis?

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.

5. In what situations would joint density be more appropriate to use?

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.

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