Bivariate Normal Experiment

Scatter plot
Distribution graph
Distribution graph

Description

The experiment generates a random point \((X, Y)\) from a bivariate normal distribution: \(X\) has mean 0 and standard deviation \(\sigma_x\); \(Y\) as mean 0 and standard deviation \(\sigma_y\); and \((X, Y)\) has correlation \(\rho\) The point is shown graphically as a red dot in the scatterplot, and the coordinates are recorded on each update. The distribution regression line is shown in blue in the scatterplot, and on each update, the sample regression line is shown in red. The probability density function and moments of \(X\) and of \(Y\) are shown in blue in the distribution graphs, and are recorded in the distribution tables. On each update, the empirical density function and moments are shown in red in the distribution graphs and are recorded in the distribution tables. The bivariate table gives the distribution and empirical covariance, correlation, regression slope, and regression intercept. The parameters \(\sigma_x\), \(\sigma_y\), and \(\rho\) can be varied with the input controls.