# Bivariate normal distribution Calculator

## Calculates the probability density function and upper cumulative distribution function of the bivariate normal distribution.

 $\normal probability\ density\\\hspace{20}f(x,y,\rho)={\large\frac{1}{2\pi\sqrt{1-\rho^2}}e^{-\frac{x^2-2\rho xy+y^2}{2(1-\rho^2)}}}\vspace{50}\\upper\ cumulative\ distribution\\\hspace{20}Q(x,y,\rho)={\large\int_{\small x}^{\hspace{25}\small\infty}\int_{\small y}^{\hspace{25}\small\infty}}f(u_1,u_2,\rho)du_1 du_2\\$

 percentile x percentile y correlation coefficient p 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Bivariate\ Standard\ Normal\ distribution\\[10](1)\qquad probability\ density\\\hspace{30}f(x,y,\rho)={\large\frac{1}{2\pi\sqrt{1-\rho^2}}e^{-\frac{x^2-2\rho xy+y^2}{2(1-\rho^2)}}}\\(2)\qquad upper\ cumulative\ distribution\\\hspace{30}Q(x,y,\rho)={\large\int_{\small x}^{\hspace{25}\small\infty}\int_{\small y}^{\hspace{25}\small\infty}}f(u_1,u_2,\rho)du_1 du_2\\$

Bivariate normal distribution
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