# Joint PDF of Random Variables X & Y -1 to 1

• vptran84
In summary, a joint probability density function (PDF) is a mathematical function that describes the probability of two random variables occurring simultaneously within a given range. It differs from a marginal PDF, which describes the probability of a single random variable occurring within a given range. The joint PDF is calculated by integrating the joint probability distribution function over the entire range of both random variables. It is closely related to the joint cumulative distribution function (CDF), which represents the probability that X and Y will both be less than or equal to a given value. The joint PDF is important in statistics and data analysis as it allows for the analysis of relationships between multiple variables and the understanding of complex data sets.
vptran84
Hi, I really need help with joint PDF, if anyone can help, that would be super!

Random Variables X and Y have joint PDF
fx,y (x, y) = 1/2 if -1 <= x <=y <= 1, and it is 0 otherwise

a) what is fy (y)?

b) what is fx|y (x|y)?

c) what is E[X|Y = y]?

for part A) i know ur suppose to take the integral with respect to dx, but I'm not sure what the limits are.

## What is a joint probability density function (PDF)?

A joint PDF is a mathematical function that describes the probability of two random variables, X and Y, occurring simultaneously within a given range.

## How is a joint PDF different from a marginal PDF?

A marginal PDF describes the probability of a single random variable occurring within a given range, while a joint PDF describes the probability of two or more random variables occurring simultaneously.

## How is the joint PDF of X & Y calculated?

The joint PDF of X & Y is calculated by integrating the joint probability distribution function over the entire range of both random variables. This results in a two-dimensional function that represents the probability of each possible combination of X and Y values.

## What is the relationship between a joint PDF and a joint CDF?

A joint CDF (cumulative distribution function) is the integral of the joint PDF. It represents the probability that X and Y will both be less than or equal to a given value. The joint PDF and CDF are closely related and can be used to calculate each other.

## Why is the joint PDF important in statistics and data analysis?

The joint PDF allows us to analyze the relationship between two or more variables and understand how they affect each other. It is commonly used in multivariate statistical analysis and is essential for understanding the probability distribution of complex data sets.

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