Finding Probability density function of a random variable with transformation

Question

Let random variable X have the probability density function

f(x)= $\frac{x}{2}$ for $0<x<2$

0 otherwise

Find the pdf of $Y=X^3$

Now I’m quite new to this, I’m trying to find $P(Y<y)$ and then finding the CDF from it integrating which I can just differentiate to get the pdf of Y but I’m not sure about the change of variable.

Answer 1

Hint:

$$P(Y\leq y)=P(X^3\leq y)=P(X\leq y^{1/3})$$