Category: Calculus
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What happens when you take the derivative of the quadratic formula? And what does it mean?
In this post, I will discuss the meaning of the three partial derivatives of the quadratic formula, with respect to each variable (a, b, and c). This is a pretty old concept of mine (I first thought about this about 6 months ago). It was also inspired by a video by blackpenredpen. However, he only…
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Formula that produces normally distributed values from uniform random variables
A few months ago, I learned this formula: R1 and R2 are independent uniformly distributed random variables between 0 and 1, and N(0,1) is a normal distribution with a mean of 0 and a standard deviation of 1. I am going to prove that this formula actually gives normally distributed values using a few other…
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Transformations of Probability Distributions
I will share an important formula which is skipped over in almost all calculus classes. It is the transformation of variables formula for a probability density function (pdf). I will derive the formula, and use it to transform a few probability distributions. Let’s call this distribution X, not to be confused with the variable x…