Ways to solve the Gaussian Integral
Introduction Assalamualaikum! It's been a while since my last post (approximately 7 months ago lol). A lot of things happens in the past 7 months! Started my MSc Statistics last September and now I am already in my second semester, Alhamdulillah! In this post, I will talk about a famous integral, which I am pretty sure most Maths BSc student encounter this in their first or second-year statistics course, the Gaussian Integral. I will show you two ways to solve this integral. The first method involves some calculus (which was my initial approach when I first encountered this integral back in my first year) while the second method is probably more intuitive. Before I start, let's look back at the form of this integral: \[ \int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}dx\] The integral above is equal to \(\sqrt{2\pi}\). Let's us show this two different ways. I used to prefer the first method since it's just evaluating integral an...