Probability Distribution Function (PDF) of a bivariate gaussian distribution

The density function describes the relative likelihood of a random variable X at a given sample. Mathematically the PDF of two variables X and Y in bivariate Gaussian distribution is given by:

where,

• μ = mean
• σ = standard deviation
• ρ = correlation of x₁ and x₂

If P = 2 then this is a bivariate gaussian distribution.

The Gaussian distribution (better known as the normal distribution) is one of the most fundamental probability distributions in statistics. A bivariate Gaussian distribution consists of two independent random variables. One can notice a bell curve while visualizing a bivariate gaussian distribution. Two random variables X₁ and X₂ are bivariate normal if aX₁+bX₂ has a normal distribution for all a, b ∈ R.