# Suppose That The Joint Pdf Of Two Random Variables X And Y Is As Follows

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- Joint distributions and independence
- Joint probability density function
- Section 4: Bivariate Distributions

*In probability theory and statistics , the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.*

When introducing the topic of random variables, we noted that the two types — discrete and continuous — require different approaches. The equivalent quantity for a continuous random variable, not surprisingly, involves an integral rather than a sum. Several of the points made when the mean was introduced for discrete random variables apply to the case of continuous random variables, with appropriate modification.

## Joint distributions and independence

Having considered the discrete case, we now look at joint distributions for continuous random variables. The first two conditions in Definition 5. The third condition indicates how to use a joint pdf to calculate probabilities. As an example of applying the third condition in Definition 5. Suppose a radioactive particle is contained in a unit square.

## Joint probability density function

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Problem Let X and Y be jointly continuous random variables with joint PDF fX,Y(x,y)={6e−(2x+3y)x,y≥00otherwise. Are X and Y independent? Find E[Y|X>2].

## Section 4: Bivariate Distributions

We'll jump in right in and start with an example, from which we will merely extend many of the definitions we've learned for one discrete random variable, such as the probability mass function, mean and variance, to the case in which we have two discrete random variables. We'll let:. If we continue to enumerate all of the possible outcomes, we soon see that the joint support S has 16 possible outcomes:. Now, because the dice are fair, we should expect each of the 16 possible outcomes to be equally likely. Here's what our joint p.

*Sheldon H. Stein, all rights reserved.*

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