Bivariate
From Rice Wiki
Consider two numerica random variables and . We can measure their covariance.
The correlation of two random variables measures the line dependent between and
Bivariate Normal
The bivariate normal (aka. bivariate gaussian) is one special type of continuous random variable.
is bivariate normal if
- The marginal PDF of both X and Y are normal
- For any , the condition PDF of given is Normal
- Works the other way around: Bivariate gaussian means that condition is satisfied
Predicting Y given X
Given bivariate normal, we can predict one variable given another. Let us try estimating the expected Y given X is x
There are three main methods
- Scatter plot approximation
- Joint PDF
- 5 statistics
5 Parameters
We need to know 5 parameters about and
If follows bivariatte normal distribution, then we have