Hey guys. I'm sure some of you are aware of how to analytically integrate e^(-x^2) dx from - infinity to infinity using polar coordinates.(adsbygoogle = window.adsbygoogle || []).push({});

I have taken that logic and showed that the integral of the normal distribution( not necessarily standard) integrates to 1 over the entire domain.

However, now I am trying the case where we integrate from - infinity to some positive number, and I am having trouble.

So lets say I know the integral of the standard normal from - infinity to 1.96 = .975. Okay, well what I am trying to do is convert the integral to polar coordinates but I am having a hard time determining the limits of integration. Is this something that just can't be done analytically?

I thought I was on to something when I had my r limits from 0 to c( and thus I would solve for c, which in turn yields a nice conversion from Cartesian to polar for limit purposes) and my theta limits from 0 to 2pi, but then I realized that the theta limit can't be 2pi because we are not. integrating to infinity wrt y.

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# Homework Help: Computing normal probability analyticallyis this possible?

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