Expectations of Joint Distribution.

In summary, a joint distribution is a probability distribution that describes the likelihood of two or more variables occurring together. It differs from a marginal distribution in that it considers the probability of multiple variables occurring together, while a marginal distribution only considers the probability of a single variable occurring. Understanding joint distributions is important in statistics as it allows for analysis of the relationship between variables and prediction of their combined outcomes. A joint distribution can also be used to calculate conditional probabilities and is represented mathematically using a joint probability mass function or joint probability density function.
  • #1
sid9221
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How would you work out E[XY] where X,Y are dependant variables in a Joint Distribution.

I know there is a relationship with the conditional distributions but I can't understand the logic behind it, hence am hoping someone here can give me directions to work out this expectation.(I don't just want a formulae, I want the idea behind it)
 
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  • #2
If you have the joint distribution, then E(XY) = integral of (xy multiplied by the joint density).
 

Related to Expectations of Joint Distribution.

1. What is a joint distribution?

A joint distribution is a probability distribution that describes the likelihood of two or more variables occurring together. It represents the relationship between two or more random variables and their possible outcomes.

2. How is a joint distribution different from a marginal distribution?

A joint distribution considers the probability of multiple variables occurring together, while a marginal distribution only considers the probability of a single variable occurring regardless of the other variables.

3. What is the significance of understanding joint distributions in statistics?

Understanding joint distributions is important in statistics because it allows us to analyze the relationship between multiple variables and make predictions about their combined outcomes. It also helps in identifying any dependencies or correlations between the variables.

4. Can a joint distribution be used to calculate conditional probabilities?

Yes, a joint distribution can be used to calculate conditional probabilities. By using the joint distribution, we can determine the probability of one variable given the value of another variable.

5. How is a joint distribution represented mathematically?

A joint distribution can be represented using a joint probability mass function for discrete variables or a joint probability density function for continuous variables. It is often denoted as P(X,Y) or f(X,Y) for two variables or P(X1,X2,...,Xn) or f(X1,X2,...,Xn) for multiple variables.

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