Continuous Random Variables 10/26

$$P(X\in dx,Y \in dy)=f(x,y)dxdy$$

The joint density is the probability per unit area near (x,y).

$$P((X,Y)\in C)=\int \int_C f(x,y)dx dy$$

The joint density is a non-negative function that integrates to 1. Distribution Function:

$$F(a,b)=\int_{-\infty}^b\int_{-\infty}^af(x,y)dxdy$$

$$f(a,b)=\frac{\partial ^2 }{\partial a \partial b} F(a,b)$$