Find the CDF of W? need to verify.

Question

My main answer for CDF is root(W)/10.

Answer 1

You really should show your working when asking people to check your work.

Your answer is correct, except you need to include the support.

$\qquad\begin{align}\mathsf P(W\leqslant w) &= \mathsf P(-\sqrt w/2\leqslant I\leqslant \sqrt w /2) \\ &= (\sqrt w /10)\,\mathbf 1_{0\leqslant \sqrt w/2\lt 5} +\mathbf 1_{5\leqslant \sqrt w/10}\\ &= (\sqrt w /10)\,\mathbf 1_{0\leqslant w\lt 100}+\mathbf 1_{100\leqslant w}\\[3ex] F_W(w) &=\begin{cases}0 &:& ~~~\qquad w\lt 0\\\sqrt w/10&:& ~~~~0\leqslant w\lt 100\\1&:& 100\leqslant w\end{cases}\end{align}$