# Which is the distribution of (X,Y) ?

• MHB
• mathmari
In summary, the conversation discusses the normal distribution of two independent variables, $X$ and $Y$, with a mean of 0 and standard deviation of 1. The distribution of $(X,Y)$ is a bivariate normal distribution and the covariance table can be obtained from the wiki article. Although $(X,Y)$ is not a linear combination of $X$ and $Y$, any linear combination of the two variables will also have a normal distribution.
mathmari
Gold Member
MHB
Hey!

We have that $X$ and $Y$ follow the normal distribution $N(0,1)$ and are independent.
1. Which is the distribution of $(X,Y)$ ?
2. Which is the covariance table of $(X,Y)$ ?

Is $(X,Y)$ related to the linear combination of $X$ and $Y$ ? (Wondering)

mathmari said:
Hey!

We have that $X$ and $Y$ follow the normal distribution $N(0,1)$ and are independent.
1. Which is the distribution of $(X,Y)$ ?
2. Which is the covariance table of $(X,Y)$ ?

Is $(X,Y)$ related to the linear combination of $X$ and $Y$ ?

Hey mathmari! (Wave)

It's a so called Bivariate normal distribution.
The section in the wiki article explains how to get the covariance table. (Thinking)

And no, $(X,Y)$ is not linear combination of $X$ and $Y$.
However, a property of a bivariate normal distribution is that any linear combination $\lambda X + \mu Y$ has a normal distribution.

## 1. What is the distribution of (X,Y)?

The distribution of (X,Y) refers to the pattern or spread of values that occur for two variables, X and Y. It shows how often each value occurs and the relationship between the two variables.

## 2. How is the distribution of (X,Y) represented?

The distribution of (X,Y) is often represented graphically using scatter plots, histograms, or box plots. These visual representations help to show the shape, center, and spread of the data.

## 3. What factors can affect the distribution of (X,Y)?

The distribution of (X,Y) can be influenced by various factors such as sample size, outliers, and the relationship between X and Y. It can also be affected by the type of distribution, such as normal, skewed, or bimodal.

## 4. How can I determine the distribution of (X,Y) from data?

To determine the distribution of (X,Y) from data, you can use descriptive statistics such as mean, median, and standard deviation. You can also create a visual representation of the data, such as a histogram, to see the shape of the distribution.

## 5. Why is it important to understand the distribution of (X,Y)?

Understanding the distribution of (X,Y) is essential for drawing conclusions and making predictions based on the data. It can also help identify any patterns or trends between the two variables and provide insight into the relationship between them.

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