# 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:

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

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*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. |