Let’s derive Chi-Squared PDF from normal distribution *intuitively*
We can calculate the probability density function (PDF) of a random variable from its cumulative distribution function (CDF) using differentiation.
Specifically, if F(x) is the CDF of a random variable X, then the PDF f(x) is:
f(x) = d/dx F(x)
In probability and statistics, it is not unusual to figure out the PDF from the CDF. In many cases, it might be easier to obtain the CDF than the PDF. In these situations, we can calculate the CDF and then use differentiation to find the PDF.