I ran into this problem.
If $ξ$ is a random variable with a standard normal distribution and η is a random variable such that: $η = \left\lbrace\right. ξ$, if $\left\|ξ\right\| \le 2$ $, -ξ$ if $\left\|ξ\right\| \gt 2$
Compute a distribution of the number variable $η$.
I am not sure whether I understand what they want me to compute. Isn't the distribution of η just a density function $φ(x) = \left(\frac{e^{-x^2/2}}{\sqrt {2\pi}}\right)$ for $x \le 2$ and $-φ(x)$ for $x \gt 2$?