Are X and Y dependent random variables?

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Start date Dec 9, 2021
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Random Random variables Variables

In summary, the relationship between X and Y determines whether they are dependent or independent random variables. This can be determined through statistical tests such as Pearson correlation coefficient or scatter plots. Dependent random variables have a statistical relationship, while independent random variables do not. However, it is possible for X and Y to be dependent in some cases and independent in others, especially if there is a non-linear relationship between them. Real-world examples of dependent random variables include height and weight, temperature and air pressure, and price and demand for a product.

Dec 9, 2021

docnet

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Homework Statement: .

Relevant Equations: .

Screen Shot 2021-12-09 at 3.31.44 AM.png

Screen Shot 2021-12-09 at 3.34.30 AM.png

(a) the agrea of the triangleses is 1, so γ one.

(b) I'm not sure how to prove. i feel like ##X## and ##Y## are dependent because ##E(Y|X=0)=\frac{1}{2}## and ##E(Y|X=1)=0## so ##Y## seems dependent on ##X##. ##f_X=1-x## for ##x>0## ane ##f_X=1+x## for ##x<0## so X seems independent on Y.

Last edited: Dec 9, 2021

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Dec 9, 2021

Orodruin

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Look fine

FAQ: Are X and Y dependent random variables?

Are X and Y dependent random variables?

The answer to this question depends on the specific variables in question and the nature of their relationship. In general, two random variables are considered dependent if the value of one variable affects the probability distribution of the other. This can be determined through statistical methods such as correlation analysis or by examining the underlying mechanisms that generate the variables.

How can I determine if X and Y are dependent random variables?

To determine the dependence between two random variables, you can use statistical tests such as Pearson's correlation coefficient or Spearman's rank correlation coefficient. These tests measure the strength and direction of the relationship between the variables. Additionally, you can also visually inspect the data or use regression analysis to identify any patterns or trends.

What is the difference between dependent and independent random variables?

Dependent random variables are those that are related to each other in some way, meaning the value of one variable affects the probability distribution of the other. On the other hand, independent random variables are not related and the value of one does not impact the other. In other words, the occurrence of one variable does not affect the probability of the other variable occurring.

Can two dependent random variables become independent?

In most cases, two dependent random variables cannot become independent. However, if the underlying relationship between the variables changes, it is possible for them to become independent. For example, if the variables were previously dependent due to a confounding variable, removing the confounding variable could make them independent.

How does the dependence between X and Y affect statistical analysis?

The dependence between two random variables can have a significant impact on statistical analysis. When variables are dependent, traditional statistical tests may not be appropriate and alternative methods must be used. Additionally, the strength and direction of the relationship between the variables should be considered when interpreting the results of the analysis.