Let $U$ be a uniform random variable on $[0,1]$. Let $X=U^3$.

Question

The function distribution would be $U \leq \sqrt[3]{x}$

Answer 1

Hint: $$ F_X(x) = \Pr(X \leq x) = \Pr(U^2 \leq x) = \Pr(-\sqrt x \leq U \leq \sqrt x). $$