Let XXX have PDF f(x)=1πe−x2f(x) = \frac{1}{\sqrt{\pi}}e^{-x^2}f(x)=π1e−x2. Is this valid?
Yes, integral is 1
No, integral not 1
Only for x∈[0,1]x \in [0,1]x∈[0,1]
Yes, but only x≥0x \geq 0x≥0