Two-Dimensional Normal Distribution
Calculate the probability density function and the upper cumulative probability for a 2-dimensional standard normal distribution.
| \(\normalsize probability\ density\\ \hspace{20px}f(x,y,\rho)={\large\frac{1}{2\pi\sqrt{1-\rho^2}}e^{-\frac{x^2-2\rho xy+y^2}{2(1-\rho^2)}}}\\ upper\ cumulative\ distribution\\ \hspace{20px}Q(x,y,\rho)={\large\int_{\small x}^{\small\infty}\int_{\small y}^{\small\infty}}f(u_1,u_2,\rho)du_1 du_2\\\) |
| \(\normalsize Bivariate\ Standard\ Normal\ distribution\\ (1) probability\ density\\ \hspace{30px}f(x,y,\rho)={\large\frac{1}{2\pi\sqrt{1-\rho^2}}e^{-\frac{x^2-2\rho xy+y^2}{2(1-\rho^2)}}}\\ (2) upper\ cumulative\ distribution\\ \hspace{30px}Q(x,y,\rho)={\large\int_{\small x}^{\small\infty}\int_{\small y}^{\small\infty}}f(u_1,u_2,\rho)du_1 du_2\\ \) |
No customer feedback for this calculation yet.