# Ch. 5 Joint Probability

Sections covered: 5.1, 5.2

## 5.1 Jointly Distributed Random Variables

Skip everything but “Two Discrete Random Variables” pp. 199-200

## 5.2 Expected Values, Covariance, and Correlation

Skip everything but “Covariance” pp. 214-215 and “Correlation” pp. 216-218

In both sections, skip double integrals. Focus on the concepts of covariance and correlation. The only formula you need to know is:

$$\rho_{X, Y} = \frac{Cov(X, Y)}{\sigma_X \cdot \sigma_Y}$$

### Interactive

Click anywhere on the graph to add points. The correlation coefficient will be calculated.

The correlation coefficient (r) is a measure of the linear relationship between two variables x and y. To get a sense of the connection between the appearance of points – (x,y) pairs – in a scatterplot and the value of r, click anywhere on the graph to add points. To remove points, click the Remove points button and then mouseover points.

 Add points  Remove points Two points are needed to calculate r.

## Resources

Correlation and Covariance Visualization

https://shiny.rit.albany.edu/stat/rectangles/