# Jointly continuous random dependent variables

• DotKite
In summary, the question is asking to find the probability of X being less than or equal to 3/4 and Y being less than or equal to 1/2, given that X and Y are random variables with a joint probability density function of 6(1-y) for 0≤x≤y≤1 and 0 elsewhere. The attempted solution involves finding the limits of integration for the dependent variables, with the possibility of the inner integral being for X and the limits being 0 to Y, and Y being 1/2 to 1.
DotKite

## Homework Statement

Let X and Y be rv's with joint pdf

f(x,y) = 6(1-y) for 0≤x≤y≤1 and 0 elsewhere

find Pr(X≤3/4, Y≤1/2)

## The Attempt at a Solution

Ok I am having trouble with finding the right limits of integration for dependent variables. If we let the inner integral be for x would the limits be 0 to y? Then would y be 1/2 to 1?

DotKite said:

## Homework Statement

Let X and Y be rv's with joint pdf

f(x,y) = 6(1-y) for 0≤x≤y≤1 and 0 elsewhere

find Pr(X≤3/4, Y≤1/2)

## The Attempt at a Solution

Ok I am having trouble with finding the right limits of integration for dependent variables. If we let the inner integral be for x would the limits be 0 to y? Then would y be 1/2 to 1?

No. Have you drawn a picture of the region?

## 1. What is the definition of jointly continuous random dependent variables?

Jointly continuous random dependent variables refer to two or more random variables that are continuous (can take on any value within a range) and are related to each other in a way that their values are not independent of each other. This means that knowing the value of one variable can provide information about the values of the other variables.

## 2. How are jointly continuous random dependent variables different from independent variables?

Jointly continuous random dependent variables are different from independent variables in that their values are not independent of each other. Independent variables do not affect each other's values, while dependent variables do. This means that the relationship between jointly continuous random dependent variables is not simply due to chance.

## 3. What is the joint probability density function of jointly continuous random dependent variables?

The joint probability density function is a function that describes the probabilities of different combinations of values for two or more random variables. It is used to determine the probability of a particular outcome occurring for a set of dependent variables, taking into account their continuous nature and their relationship with each other.

## 4. Can jointly continuous random dependent variables be correlated?

Yes, jointly continuous random dependent variables can be correlated. Correlation refers to the strength and direction of the relationship between variables. In the case of dependent variables, correlation measures the strength and direction of the relationship between their values.

## 5. How are jointly continuous random dependent variables used in statistical analysis?

Jointly continuous random dependent variables are used in statistical analysis to model complex relationships between variables. They are often used in regression analysis, where one variable (the dependent variable) is predicted based on the values of one or more other variables (the independent variables). They are also used in multivariate analysis, where the relationships between multiple dependent variables are examined simultaneously.

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