How do one go about solving this tricky question:
Given the pdf of $k_{o}$ as shown below $$f_{k_{o}}(k)=2\pi v ke^{-\pi v k^{2}}, \quad 0\leq k\leq \infty $$
and $q$ is given as $$ q = \zeta_{o} k_{o}^{n}, \quad 0\leq q\leq q_{u}$$ Prove that the pdf of $q$ is given as $$\eqalign{f_{q}(x) = &\, {2\pi v x^{{2 \over \eta} - 1}e^{-\pi v \left({x \over \zeta_{o}}\right)^{2 \over \eta}} \over \eta\zeta_{o}^{2 \over \eta}\int\limits_{0}^{q_{u}}{2\pi v \over \eta\zeta_{o}^{2 \over \eta}}y^{{2 \over \eta} - 1}e^{-\pi v \left({y\over\zeta_{o}}\right)^{2\over\eta}}\,\mathrm{d}y}\cr =& \, {2\pi v x^{{2 \over\eta}-1}e^{-\pi v \left({x\over\zeta_{o}}\right)^{2\over\eta}}\over\eta\zeta_{o}^{2\over\eta}\left(1 - e^{-\pi v \left({q_{u} \over \zeta_{o}}\right)^{2 \over \eta}}\right)}.\quad 0 \leq x\leq q_{u}.}$$
