How to find densitiy of |X| Let $X \sim \operatorname{N}\left(0,1\right)$ be a standard normal distributed random variable: Can someone please please show me the whole way how to find the density of $\left\vert X\right\vert$. My tries: I saw sites where someone gives tips and I wanna do it with Cumulative distribution function but everywhere are only few tips and I didn't understand it. Can someone please explain how to do it for someone who never did tasks with densities before? I only know the density of $X$ :  I would be very thankful for help.
P.d.f of the absolute value of a normally distributed variable I came across this question as an exercise, had a brief idea, but didn't know how to proceed.     Let $X \sim N(0, 1)$. What is the p.d.f of $|X|$ ?   I know the final p.d.f looks just like the right half of the original pdf, but extended vertically for a factor of 2.  Could someone please show mathematically what the p.d.f of variable |X| is going to be, and explain briefly? Thank you.
Intuitive explanation of convergence in distribution and convergence in probability What is the intuitive difference between a random variable converging in probability versus a random variable converging in distribution?  I've read numerous definitions and mathematical equations, but that does not really help. (Please keep in mind, I am undergraduate student studying econometrics.)  How can a random variable converge to a single number, but also converge to a distribution?