Mean and Covariance Simulation
Interactive visualization of bivariate normal distributions
Distribution Parameters
Mean X (μ₁):
7
Mean Y (μ₂):
7
Variance X (σ₁²):
4
Variance Y (σ₂²):
4
Covariance (σ₁₂):
2
Generate Data
Reset
Animate Changes
Visualization Options
Show Principal Axes
Show Density Contours
Distribution Properties
Eigenvalue 1:
4.00
Eigenvalue 2:
2.00
Principal Angle:
45.0°
Correlation:
0.500
Enhanced Interactions
Color Theme
Animation Pattern
Circular Motion
Oscillating
Spiral
Random Walk
Sample Size:
300
Visualization Mode
Enable 3D View
Toggle between 2D and 3D visualization
Point Interaction
Enable Point Dragging
Drag points to see how they affect the distribution
Animation Speed:
5
Switch to 2D
Presets
Try these example distributions:
Circular
Horizontal Ellipse
Diagonal (45°)
Narrow (135°)
Assignment
Create distributions with specific shapes and orientations
Manipulate the covariance matrix to achieve a 30° orientation
Find parameters for a very narrow, elongated distribution
Document how eigenvalues relate to the shape of the ellipses