Probability Inside a Unit Area Circle |Bivariate Standard Normal | UPSC ISS 2023 Paper-1| Problem-7

Описание: This video explores the integral of the joint PDF of two independent standard normal variables \(X\) and \(Y\) over a unit area circle centered at the origin. Using polar coordinates and the Jacobian transformation, we calculate the probability that the point \((X, Y)\) lies inside the circle with radius \(\frac{1}{\sqrt{\pi}}\). The result shows the probability is \(1 - e^{-1/2\pi}\), demonstrating an important application of multivariate normal distribution and integration techniques. This is valuable for UPSC aspirants and statistics students focusing on bivariate distributions and polar coordinate integration.

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