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.